text:
## Problem of the Week

How many integers $m$ and $n$ are there such that $m+n=mn$?

Due Wednesday, March 29 at midnight submitted to this Google form. You must be logged into your NAU gmail to submit via this form. If you are having trouble with the form, feel free to email a solution to Rachel.Neville@nau.edu

Rules for Problem of the Week

The contest is open to all undergraduates at Northern Arizona University. Solutions are due at midnight of every Wednesday.

Submit your solutions to this Google form as a pdf or jpg of either typed or neatly handwritten and scanned work. If you don't have access to a scanner use a phone app like CamScanner or Adobe Scan.

**The answers should be clearly and logically explained. ** The goal is to write mathematics, not to to write down the answer and draw a box around it.

Send your questions to Rachel Neville at Rachel.Neville@nau.edu. If your instructor gives you credit for submissions to problem of the week, please include their name and the class in the form (e.g. Swift, MAT 239) the first time you submit a solution. (After that I have the information in my spreadsheet.)

Problems will be graded on a scale of 1 to 3. A model solution is posted each week. A ladder listing the points earned is posted in the lobby of the Adel Math Building (across from the MAP room). Your name will be printed on the ladder, but no names will be published on the web. Let me know if you want to remain anonymous on the posted ladder and what name you would prefer to use.


text:
## How to solve kinematics problems

Hi, all here in this article I am giving some tips and tricks to solve kinematics problems. To master problem-solving skill you need to practice more and more problems as said practice makes a man perfect. Look at examples in…

## Centre of mass formula list with solved examples and problems

This article contains a list of center of mass formulas along with some center of mass problems and examples. Center of mass formula list For a system of N particles,the position vector of center of mass is $\vec{R}_{CM}=\frac{m_1\vec{r}_1+m_2\vec{r}_2+………..+m_N\vec{r}_N}{m_1+m_2+…..+m_N}=\frac{\sum_{i=1}^N{m_i\vec{r}_i}}{M}$ The position…

## Electric charge concept

In this article learn about electrical or electric charge concepts with the help of some questions and answers.Diverse phenomenons known in nature are based on four fundamental interactions among particles and they are Strong interactions Weak interactions Electromagnetic interactions Gravitational…

## Thermodynamics Multiple Choice Questions and Answers

PART A Question 1 In a given process on an ideal gas, $dW>0$ and $dQ=0$.Then for the gasa) Temperature will decreaseb) Temperature will increasec) volume will decreased) none of above Question 2A cylinder of diameter $D$ and of thermal conductivity…

## Coherent Sources of light

Coherent sources are those sources of light that emit continuous light waves of the same wavelength, same frequency, and are in the same phase or have a constant phase difference. For observing the interference phenomenon coherence of light waves is…

## The maximum range of projectile formula

Let us consider a projectile projected with initial velocity $$v_{0}$$ making an angle $$\theta_0$$ with the horizontal as shown below in the figure. We know that the horizontal range of a projectile is the distance traveled by the projectile during…

## Current electricity equations and formulas (Direct Current)

In this article find the list of current electricity equations or current electricity formulas. Current electricity is related to the flow of electrons. Current electricity is of two types: DC or direct current  AC or alternating current In this article,…

## Tricks to solve pulley problems

A lot of problems in mechanics involves string, pulley and springs for example masses are attached to string or spring and so on. Here in this article learn about some Tricks to solve pulley problems .Here find the concepts you need to…

format: plain


text:
My Math Forum Rolle's Theorem

 Calculus Calculus Math Forum

 October 5th, 2012, 07:20 PM #1 Senior Member   Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0 Rolle's Theorem y = f(x) = (x-3) (x+1)^(2) on [-1,3] closed interval Can Rolle's Theorem be applied to this function on [1,3] I said Yes because I set each to zero and got zero for both therefore if f '(a) = f '(b) then f '(c) must exist please someone check to see if I did this properly Next it says if Rolle's Theorem can be applied, find all values, C, in the open interval (-1,3) such that f ' (c) = 0 I need some help with this second question
October 5th, 2012, 08:55 PM   #2
Senior Member

Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,211
Thanks: 521

Math Focus: Calculus/ODEs
Re: Rolle's Theorem

Rolle's theorem states:

Quote:
 Let $f$ be a function that is continuous on $[a,b]$ and differentiable on $(a,b)$. If $f(a)=f(b)=0$, then there exists a number $c$ in $(a,b)$ such that $f'(c)=0$.
Since:

$f(-1)=f(3)=0$, and the function is continuous and differentiable for all reals (and so it is thus on the given interval) we know by Rolle's theorem there is at least one critical number on the given interval.

To find the critical number(s), we equate the derivative to zero, and solve for $x$.

$f(x)=(x-3)(x+1)^2$

Using the product rule, we find:

$f'(x)=(x-3)$$2(x+1)$$+(1)(x+1)^2=(x+1)$$2(x-3)+(x+1)$$=(x+1)(3x-5)=0$

We discard the root $x=-1$ as it is an end-point of the interval, and we find:

$c=\frac{5}{3}$

 October 6th, 2012, 07:17 AM #3 Senior Member   Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0 Re: Rolle's Theorem Follow

 Tags rolle, theorem

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Shamieh Calculus 4 October 21st, 2013 04:18 PM bobcantor1983 Calculus 1 October 1st, 2013 01:49 PM joeljacks Calculus 6 October 28th, 2012 05:30 PM mathkid Calculus 4 October 6th, 2012 06:35 PM maximus101 Real Analysis 4 February 11th, 2011 08:42 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top


text:
## Basic Orientation Matrix Question

Hi all,

I am the author of bvhacker, a free animation application (see here: www.bvhacker.com)

I'm currently working on a new release, and am trying to change the orientation of bones in a bvh animation file. My problem is this:

I have a bvh file that has it's arms aligned down the y-axis. I need to convert it so that it's arms are aligned along the x-axis.

Or, put another way, when all joint's rotations are set to zero, the figure's arms are by it's sides. I need the figure's arms to be outstreched horizontally when zeroed out.

When I first encountered the problem I tried the naive solutions - e.g. just rotating the arms through 90 degrees. Of course, this didn't work well!

I've researched this as far as I can on the web. The solution *appears* to be in changing the arm bones initial translations from 0,L,0 to L,0,0 (where L represents the length of the arm) and then multiplying all my XYZ rotation data values in turn, each rotation value represented by a 4-element vector (where w=1), by a 4x4 'orientation matrix'. I'm fairly comfortable implementing this in code, but I have no idea of the values that should go into the orientation matrix, other than as follows ('u' is for unknown value)

u u u 0
u u u 0
u u u 0
0 0 0 1

I did study matrix transformations at uni, but it was a long time ago now, and I didn't get a really good grasp on the subject at the time! Can anyone help?

Cheers,

:-Davedub


text:
Deals Of The Week - hours only!Up to 80% off on all courses and bundles.-Close
Introduction
Challenge with artists
Challenge with orchestras

## Instruction

Welcome to the next part of the challenge! As in the previous part, you've already worked with three out of four of the tables here, so this will serve as a quick refresher.

## Exercise

Select all data from the Orchestras table. As you can see, it consists of the following columns:

• Id – the ID of a given orchestra,
• Name – the name of a given orchestra,
• MembersNumber – the total number of members of a given orchestra,
• Rating – the average rating of a given orchestra over the last ten years,
• CityOrigin – the city from which a given orchestra originates,
• CountryOrigin – the country of origin of a given orchestra,
• YearOrigin – year in which a given orchestra was created.


text:
# 6.2 What is the role of depressant in froth floatation process?

Role of depressant in froth flotation method is to separate two sulphid ores by adjusting one ore to form froth. For example- $NaCN$ is used as a depressant it selectively prevents $ZnS$ to coming to the froth but allows PbS with the froth. NaCN react with $ZnS$ to form $Na_{2}[Zn(CN)_{4}]$
$4NaCN+ ZnS\rightarrow Na_{2}[Zn(CN)_{4}]+ Na_{2}S$


text:
# Index of dispersion

(Redirected from Variance-to-mean ratio)

In probability theory and statistics, the index of dispersion,[1] dispersion index, coefficient of dispersion, or variance-to-mean ratio (VMR), like the coefficient of variation, is a normalized measure of the dispersion of a probability distribution: it is a measure used to quantify whether a set of observed occurrences are clustered or dispersed compared to a standard statistical model.

It is defined as the ratio of the variance $\sigma^2$ to the mean $\mu$,

$D = {\sigma^2 \over \mu }.$

It is also known as the Fano factor, though this term is sometimes reserved for windowed data (the mean and variance are computed over a subpopulation), where the index of dispersion is the special case where the window is infinite. Windowing data is frequently done: the VMR is frequently computed over various intervals in time or small regions in space, which may be called "windows", and the resulting statistic called the Fano factor.

It is only defined when the mean $\mu$ is non-zero, and is generally only used for positive statistics, such as count data or time between events, or where the underlying distribution is assumed to be the exponential distribution or Poisson distribution.

## Terminology

In this context, the observed dataset may consist of the times of occurrence of predefined events, such as earthquakes in a given region over a given magnitude, or of the locations in geographical space of plants of a given species. Details of such occurrences are first converted into counts of the numbers of events or occurrences in each of a set of equal-sized time- or space-regions.

The above defines a dispersion index for counts.[2] A different definition applies for a dispersion index for intervals,[3] where the quantities treated are the lengths of the time-intervals between the events, and where the index is equivalent to the square of the coefficient of variation of the interval lengths. Common usage is that "index of dispersion" means the dispersion index for counts.

## Interpretation

Some distributions, most notably the Poisson distribution, have equal variance and mean, giving them a VMR = 1. The geometric distribution and the negative binomial distribution have VMR > 1, while the binomial distribution has VMR < 1, and the constant random variable has VMR = 0. This yields the following table:

Distribution VMR
constant random variable VMR = 0 not dispersed
binomial distribution 0 < VMR < 1 under-dispersed
Poisson distribution VMR = 1
negative binomial distribution VMR > 1 over-dispersed

This can be considered analogous to the classification of conic sections by eccentricity; see Cumulants of particular probability distributions for details.

When the coefficient of dispersion is less than 1, a dataset is said to be "under-dispersed": this condition can relate to patterns of occurrence that are more regular than the randomness associated with a Poisson process. For instance, points spread uniformly in space or regular, periodic events will be under-dispersed.

If the index of dispersion is larger than 1, a dataset is said to be over-dispersed: this can correspond to the existence of clusters of occurrences. Clumped, concentrated data is over-dispersed.

In terms of the interval-counts, over-dispersion corresponds to there being more intervals with low counts and more intervals with high counts, compared to a Poisson distribution: in contrast, under-dispersion is characterised by there being more intervals having counts close to the mean count, compared to a Poisson distribution.

The relevance of the index of dispersion is that it has a value of one when the probability distribution of the number of occurrences in an interval is a Poisson distribution. Thus the measure can be used to assess whether observed data can be modeled using a Poisson process.

A sample-based estimate of the dispersion index can be used to construct a formal statistical hypothesis test for the adequacy of the model that a series of counts follow a Poisson distribution.[4][5]

The VMR is a good measure of the degree of randomness of a given phenomenon. This technique is also commonly used in currency management.

## Example

For randomly diffusing particles (Brownian motion), the distribution of the number of particle inside a given volume is poissonian, i.e. VMR=1. Therefore, to assess if a given spatial pattern (assuming you have a way to measure it) is due purely to diffusion or if some particle-particle interaction is involved : divide the space into patches, Quadrats or Sample Units (SU), count the number of individuals in each patch or SU, and compute the VMR. VMRs significantly higher than 1 denote a clustered distribution, where random walk is not enough to smother the attractive inter-particle potential.

## Statistics

The first to discuss the use of a test to detect deviations from a Poisson or binomial distribution appears to have been Lexis in 1877. One of the tests he developed was the Lexis ratio.

This index was first used in botany by Clapham in 1936.

If the variates are Poisson distributed then the index of dispersion is distributed as a χ2 statistic with n - 1 degrees of freedom when n is large and is μ > 3.[6] For many cases of interest this approximation is accurate and Fisher in 1950 derived an exact test for it.

Hoel studied the first four moments of its distribution.[7] He found that the approximation to the χ2 statistic is reasonable if μ > 5.

## Notes

1. ^ Cox &Lewis (1966)
2. ^ Cox & Lewis (1966), p72
3. ^ Cox & Lewis (1966), p71
4. ^ Cox & Lewis (1966), p158
5. ^ Upton&Cook(2006), under index of dispersion
6. ^ Frome, E. L. (1982). "Algorithm AS 171: Fisher's Exact Variance Test for the Poisson Distribution". Journal of the Royal Statistical Society, Series C 31 (1): 67–71. JSTOR 2347079.
7. ^ Hoel, P. G. (1943). "On Indices of Dispersion". Annals of Mathematical Statistics 14 (2): 155–162. JSTOR 2235818.

## References

• Cox, D. R.; Lewis, P. A. W. (1966). The Statistical Analysis of Series of Events. London: Methuen.
• Upton, G.; Cook, I. (2006). Oxford Dictionary of Statistics (2nd ed.). Oxford University Press. ISBN 978-0-19-954145-4.


text:
# Question #c3c9a

Feb 23, 2017

Depends on what you are given.

#### Explanation:

If you are simply asked to give the scientific notation of a number, say 0.00000016, the decimal point ends up right after the FIRST whole number (except zero).

0.00000016 = $1.6$ x ${10}^{- 7}$
1,234,567,890 = $1.23$ x ${10}^{9}$

The movement of decimal depends on what numbers you were given. A $\textcolor{b l u e}{p o s i t i v e}$ exponent would mean that you have shifted the decimal from right to left.

1,000,000 = $1.0$ x ${10}^{6}$
213,645.89 = $2.14$ x ${10}^{5}$

A $\textcolor{red}{\text{negative}}$ movement means that the decimal place moved from left to right.

0.004 = $4.0$ x ${10}^{- 2}$
0.00435 = $4.35$ x ${10}^{- 2}$


text:
# Radial limits of harmonic conjugate and Hilbert transform

Let $\mu$ be a real measure on the circle $\mathbf{T}$. Then the function $$f(z)=\int_\mathbf{T} \mathrm{Im}\left(\frac{\zeta+z}{\zeta-z}\right) d\mu(\zeta)$$ is harmonic on the unit disc and its radial limits exist almost everywhere.

Does the Hilbert transform of $\mu$ equal the radial limit function of $f$ on $\mathbf{T}$ almost everywhere and why?

The Hilbert transform of $\mu$ is $$(H\mu)(z)=p.v.\frac{1}{\pi}\int_\mathbf{T}\frac{d\mu(\zeta)}{z-\zeta}$$ for $z\in\mathbf{T}$. (Please check, I'm not sure)

I have come so far to see, that the Hilbert transform and the radial limits of $f$ behave somewhat similarly as can be seen from noting that $$\mathrm{Im}\left(\frac{e^{it}+re^{is}}{e^{it}-re^{is}}\right)\rightarrow \cot(s/2)$$ as $r\rightarrow 1$ and $\cot(s/2)$ behaves similarly as $2/s$ when $|s|$ is small.

(I would also appreciate if somebody knew the answer just for the case that $\mu$ has continuous density w.r.t. the Lebesgue measure on $\mathbf{T}$ or similar special cases.)

-

## 1 Answer

Your definition of the Hilbert transform on the unit circle is not correct, but the answer to your question is positive. Check for instance Chapter 11.5 in "Inequalities: A Journey into Linear Analysis" for a definition of the Hilbert transform on the circle and properties for some functional analytical spaces.

-
Thanks a lot! I knew there was something wrong with the definition I had. –  Your Ad Here Nov 4 '12 at 16:28


text:
How do i answer this?  int_2^4 \ (2x)/(x^2+1)  via a Riemann sum.

Nov 20, 2017

 A = lim_(n rarr oo) \ sum_(i=1)^n 2/n \ (2((2n+2i)/n)) / (( (2n+2i)^2/n^2 + 1)

$\setminus \setminus \setminus = {\lim}_{n \rightarrow \infty} \setminus {\sum}_{i = 1}^{n} \frac{4 \left(2 n + 2 i\right)}{{\left(2 n + 2 i\right)}^{2} + {n}^{2}}$

Explanation:

We seek:

${\int}_{2}^{4} \setminus \frac{2 x}{{x}^{2} + 1}$

via a Riemann sum. So, we have:

$A = {\lim}_{n \rightarrow \infty} \setminus {\sum}_{i = 1}^{n} f \left({x}_{i}\right) \Delta x$
$\setminus \setminus \setminus = {\lim}_{n \rightarrow \infty} \setminus {\sum}_{i = 1}^{n} f \left(a + i \Delta x\right) \Delta x$
$\setminus \setminus \setminus = {\lim}_{n \rightarrow \infty} \setminus {\sum}_{i = 1}^{n} f \left(2 + \frac{\left(4 - 2\right) i}{n}\right) \frac{4 - 2}{n}$
$\setminus \setminus \setminus = {\lim}_{n \rightarrow \infty} \setminus {\sum}_{i = 1}^{n} f \left(2 + \frac{2 i}{n}\right) \frac{2}{n}$
$\setminus \setminus \setminus = {\lim}_{n \rightarrow \infty} \setminus {\sum}_{i = 1}^{n} \frac{2}{n} \setminus f \left(\frac{2 n + 2 i}{n}\right)$

Then using the definition of $f \left(x\right) = \frac{2 x}{{x}^{2} + 1}$ this becomes:

$A = {\lim}_{n \rightarrow \infty} \setminus {\sum}_{i = 1}^{n} \frac{2}{n} \setminus \frac{2 \left(\frac{2 n + 2 i}{n}\right)}{{\left(\frac{2 n + 2 i}{n}\right)}^{2} + 1}$

for a 1 mark question this answer is probably sufficient, but it could be simplified further if required:

 A = lim_(n rarr oo) \ sum_(i=1)^n 2/n \ (2((2n+2i)/n)) / (( (2n+2i)^2/n^2 + n^2/n^2)

$\setminus \setminus \setminus = {\lim}_{n \rightarrow \infty} \setminus {\sum}_{i = 1}^{n} \frac{4 \left(\frac{2 n + 2 i}{n} ^ 2\right)}{\frac{{\left(2 n + 2 i\right)}^{2} + {n}^{2}}{n} ^ 2}$

$\setminus \setminus \setminus = {\lim}_{n \rightarrow \infty} \setminus {\sum}_{i = 1}^{n} \frac{4 \left(2 n + 2 i\right)}{{\left(2 n + 2 i\right)}^{2} + {n}^{2}}$


text:
# Flex lexical analyser

Developer(s) Vern Paxson 2.5.39 / March 26, 2014 Unix-like Lexical analyzer generator BSD license flex.sourceforge.net

Flex (fast lexical analyzer generator) is a free software alternative to lex.[1] It is a computer program that generates lexical analyzers ("scanners" or "lexers").[2][3] It is frequently used with the free Bison parser generator. Unlike Bison, flex is not part of the GNU Project.[4]

## History

Flex was written in C by Vern Paxson around 1987.[5] He was translating a Ratfor generator, which had been led by Jef Poskanzer.[6]

## Example lexical analyzer

This is an example of a Flex scanner for the instructional programming language PL/0.

The tokens recognized are: '+', '-', '*', '/', '=', '(', ')', ',', ';', '.', ':=', '<', '<=', '<>', '>', '>='; numbers: 0-9 {0-9}; identifiers: a-zA-Z {a-zA-Z0-9} and keywords: begin, call, const, do, end, if, odd, procedure, then, var, while.

%{
#include "y.tab.h"
%}

digit         [0-9]
letter        [a-zA-Z]

%%
"+"                  { return PLUS;       }
"-"                  { return MINUS;      }
"*"                  { return TIMES;      }
"/"                  { return SLASH;      }
"("                  { return LPAREN;     }
")"                  { return RPAREN;     }
";"                  { return SEMICOLON;  }
","                  { return COMMA;      }
"."                  { return PERIOD;     }
":="                 { return BECOMES;    }
"="                  { return EQL;        }
"<>"                 { return NEQ;        }
"<"                  { return LSS;        }
">"                  { return GTR;        }
"<="                 { return LEQ;        }
">="                 { return GEQ;        }
"begin"              { return BEGINSYM;   }
"call"               { return CALLSYM;    }
"const"              { return CONSTSYM;   }
"do"                 { return DOSYM;      }
"end"                { return ENDSYM;     }
"if"                 { return IFSYM;      }
"odd"                { return ODDSYM;     }
"procedure"          { return PROCSYM;    }
"then"               { return THENSYM;    }
"var"                { return VARSYM;     }
"while"              { return WHILESYM;   }
{letter}({letter}|{digit})* {
yylval.id = strdup(yytext);
return IDENT;      }
{digit}+             { yylval.num = atoi(yytext);
return NUMBER;     }
[ \t\n\r]            /* skip whitespace */
.                    { printf("Unknown character [%c]\n",yytext[0]);
return UNKNOWN;    }
%%

int yywrap(void){return 1;}

## Internals

Main article: Lexical analysis

These programs perform character parsing, and tokenizing via the use of a deterministic finite automaton (DFA). A DFA is a theoretical machine accepting regular languages. These machines are a subset of the collection of Turing machines. DFAs are equivalent to read-only right moving Turing machines. The syntax is based on the use of regular expressions. See also nondeterministic finite automaton.

## Issues

### Time complexity

A Flex lexical analyzer usually has time complexity $O(n)$ in the length of the input. That is, it performs a constant number of operations for each input symbol. This constant is quite low: GCC generates 12 instructions for the DFA match loop. Note that the constant is independent of the length of the token, the length of the regular expression and the size of the DFA.

However, one optional feature of Flex can cause Flex to generate a scanner with non-linear performance: The use of the REJECT macro in a scanner with the potential to match extremely long tokens. In this case, the programmer has explicitly told flex to "go back and try again" after it has already matched some input. This will cause the DFA to backtrack to find other accept states. The REJECT feature is not enabled by default, and because of its performance implications its use is discouraged in the Flex manual.[7]

### Reentrancy

By default the scanner generated by Flex is not reentrant. This can cause serious problems for programs that use the generated scanner from different threads. To overcome this issue there are options that Flex provides in order to achieve reentrancy. A detailed description of these options can be found in the Flex manual.[8]

### Usage under non-Unix environments

Normally the generated scanner contains references to unistd.h header file which is Unix specific. To avoid generating code that includes unistd.h, %option nounistd should be used. Another issue is the call to isatty (a Unix library function), which can be found in the generated code. The %option never-interactive forces flex to generate code that doesn't use isatty. These options are detailed in the Flex manual.[9]

### Using flex from other languages

Flex can only generate code for C and C++. To use the scanner code generated by flex from other languages a language binding tool such as SWIG can be used.

## Flex++

A similar lexical scanner for C++ is flex++, which is included as part of the flex package. At the moment, flex supports generating code only for C and C++. The generated code does not depend on any runtime or external library except for a memory allocator (malloc or a user-supplied alternative) unless the input also depends on it. This can be useful in embedded and similar situations where traditional operating system or C runtime facilities may not be available.

The flex++ classes and code require a C++ compiler to create lexical and pattern-matching programs. The flex++ generated C++ scanner includes the header file FlexLexer.h, which defines the interfaces of the two C++ generated classes.

## References

1. ^ Levine, John R.; Mason, Tony; Brown, Doug (1992). lex & yacc (2 ed.). O'Reilly. p. 279. ISBN 1-56592-000-7. "A freely available version of lex is flex."
2. ^ Levine, John R.; Mason, Tony; Brown, Doug (1992). lex & yacc (2 ed.). O'Reilly. pp. 1–2. ISBN 1-56592-000-7.
3. ^ Levine, John (August 2009). flex & bison. O'Reilly Media. p. 304. ISBN 978-0-596-15597-1.
4. ^ Is flex GNU or not?, flex FAQ
5. '^ Levine, John (August 2009). flex & bison. O'Reilly Media. p. 9. ISBN 978-0-596-15597-1. "In about 1987, Vern Paxson of the Lawrence Berkeley Lab took a version of lex written in ratfor (an extended Fortran popular at the time) and translated it into C, calling it flex, for Fast Lexical Analyzer Generator.'"
6. ^ When was flex born?, flex FAQ
7. ^ "Performance - Lexical Analysis With Flex, for Flex 2.5.37". Flex.sourceforge.net. Retrieved 2013-02-25.
8. ^ "Reentrant - Lexical Analysis With Flex, for Flex 2.5.37". Flex.sourceforge.net. Retrieved 2013-02-25.
9. ^ "Code-Level And API Options - Lexical Analysis With Flex, for Flex 2.5.37". Flex.sourceforge.net. Retrieved 2013-02-25.


text:
# Hexagon ABCDEF

In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.

Correct result:

o =  27.713 cm
S =  55.426 cm2

#### Solution:

$u=8 \ \text{cm} \ \\ n=6 \ \\ A=360/n=360/6=60 \ ^\circ \ \\ \ \\ \sin A=u/2 : a \ \\ \ \\ a=\dfrac{ u }{ 2 } / \sin A ^\circ =\dfrac{ u }{ 2 } / \sin 60^\circ \ =\dfrac{ 8 }{ 2 } / \sin 60^\circ \ =\dfrac{ 8 }{ 2 } / 0.866025=4.6188 \ \\ \ \\ o=n \cdot \ a=6 \cdot \ 4.6188=16 \ \sqrt{ 3 }=27.713 \ \text{cm}$
$S_{1}=a^2 \cdot \ \dfrac{ \sqrt{ 3 } }{ 4 }=4.6188^2 \cdot \ \dfrac{ \sqrt{ 3 } }{ 4 } \doteq 9.2376 \ \text{cm}^2 \ \\ \ \\ S=n \cdot \ S_{1}=6 \cdot \ 9.2376=32 \ \sqrt{ 3 }=55.426 \ \text{cm}^2$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Tips to related online calculators

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

• Wall height
Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height w = 20 cm.
• Regular n-gon
In a regular n-angle polygon the internal angle is 144 degrees. Find the number n indicating the number of sides of this polygon.
• Isosceles right triangle
Contents of an isosceles right triangle is 18 dm2. Calculate the length of its base.
• Three sides
Side b is 2 cm longer than side c, side a is 9 cm shorter than side b. The triangle circumference is 40 cm. Find the length of sides a, b, c . .. .
• Alfa, beta, gama
In the triangle ABC is the size of the internal angle BETA 8 degrees larger than the size of the internal angle ALFA and size of the internal angle GAMA is twice the size of the angle BETA. Determine the size of the interior angles of the triangle ABC.
• Trapezoid - RR
Find the area of the right angled trapezoid ABCD with the right angle at the A vertex; a = 3 dm b = 5 dm c = 6 dm d = 4 dm
• Bisectors
As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6. Find the perimeter of triangle △ BDE.
• Right triangle
Ladder 16 feet reaches up 14 feet on a house wall. The 90-degree angle at the base of the house and wall. What are the other two angles or the length of the leg of the yard?
• Clock face
clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles.
• The farmer
The farmer would like to first seed his small field. The required amount depends on the seed area. Field has a triangular shape. The farmer had fenced field, so he knows the lengths of the sides: 119, 111 and 90 meters. Find a suitable way to determine t
• Horses playground
The fence for the horses has the shape of a rectangular trapezoid with an area of 400 m2, the base lengths should be 31 m and 19 m. How many meters of boards will they need to fence it if the boards are stacked in 5 rows?
• Perimeter of RT
Find the circumference of the rectangular triangle if the sum of its legs is 22.5 cm and its area is 62.5 cm2.
• Reference angle
Find the reference angle of each angle:
• Holidays - on pool
Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
• Land
Rectangular triangular land has area 30 square meters and 12 meters long leg. How many meters of the fence do you need for fencing this land?
• Maple
Maple peak is visible from a distance 3 m from the trunk from a height of 1.8 m at angle 62°. Determine the height of the maple.
• In a 2
In a thirteen sided polygon, the sum of five angles is 1274°, four of the eight angles remaining are equal and the other four are 18° less than each of the equal angles. Find the angles. .


text:
Question ee73c

Jan 22, 2016

Here's what I got.

Explanation:

Ok, here's my take on this. The way I see it, you are actually supposed to determine the molecular mass of the compound, not its molecular formula.

In order to calculate its molecular formula you need to have some information about its percent composition. This will allow you to find its empirical formula first, then use its molecular mass to find its molecular formula.

Also, I am not really sure what aqueous tension means, although I do suspect that it's actually the vapor pressure of water vapor at that temperature, i.e. ${14}^{\circ} \text{C}$.

http://www.endmemo.com/chem/vaporpressurewater.php

So, the idea here is that this problem is probably based on a Victor Meyer experiment, a laboratory technique used to find the molecular mass of a volatile compound.

The working principle revolves around the idea that the vapor of the unknown compound will displace an equal volume of dry air, which is then collected over water forming wet air.

A Victor Meyer apparatus

Your ultimate goal here will be to find the number of moles of your unknown substance present in the volume of vapor that displaced the dry air, not the wet air.

The easiest way to do that is to use the molar volume of a gas at STP. More specifically, you know that one mole of any ideal gas occupies exactly $\text{22.7 L}$ at STP conditions, which imply

• a pressure of $\text{100 kPa}$
• a temperature of ${0}^{\circ} \text{C}$

The first important thing to keep in mind here is that air collected over water is actually a mixture of dry air, which is what was displaced by the vapor of your substance, and water vapor.

This means that the pressure of wet air will be

${P}_{\text{wet air" = P_"dry air" + P_"water vapor}}$

The partial pressure of dry air will be, using the vapor pressure of water at ${14}^{\circ} \text{C}$

${P}_{\text{dry air" = "725 mmHg" - overbrace("12 mmHg")^(color(purple)("vapor pressure of water")) = "713 mmHg}}$

Now, you know that the substance displaced a volume of ${\text{24.2 cm}}^{3}$ of dry air at $\text{713 mmHg}$ and ${14}^{\circ} \text{C}$. To get the volume of the gas at STP, use the combined gas law equation

$\textcolor{b l u e}{\frac{{P}_{1} {V}_{1}}{T} _ 1 = \frac{{P}_{2} {V}_{2}}{T} _ 2}$

Do not forget to use matching units for this! Also, the temperature must be expressed in Kelvin! Rearrange the equation to solve for ${V}_{2}$, the volume of dry air at STP

${V}_{2} = {P}_{1} / {P}_{2} \cdot {T}_{2} / {T}_{1} \cdot {V}_{1}$

You can go from mmHg to kPa by going through atm first.

713 color(red)(cancel(color(black)("mmHg"))) * (1color(red)(cancel(color(black)("atm"))))/(760color(red)(cancel(color(black)("mmHg")))) * "101.325 kPa"/(1color(red)(cancel(color(black)("atm")))) = 711/760 * "101.325 kPa"

This means that you'll have

V_2 = (713/760 * 101.325 color(red)(cancel(color(black)("kPa"))))/(100color(red)(cancel(color(black)("kPa")))) * ((0 + 273.15)color(red)(cancel(color(black)("K"))))/((273.15 + 14)color(red)(cancel(color(black)("K")))) * "24.2 cm"^3

${V}_{2} = {\text{21.883 cm}}^{3}$

So, your unknown substance displaced ${\text{21.883 cm}}^{3}$ of dry air at STP. This of course implies that the volume of its vapor will be

${V}_{\text{substance" = V_"dry air" = "21.883 cm}}^{3}$

The number of moles of your substance present in

$\text{21.883 cm"^3 = "21.883 mL}$

of vapor at STP will thus be

21.883 color(red)(cancel(color(black)("mL"))) * (1 color(red)(cancel(color(black)("L"))))/(10^3color(red)(cancel(color(black)("mL")))) * overbrace("1 mole"/(22.7color(red)(cancel(color(black)("L")))))^(color(purple)("molar volume of a gas")) = "0.00096401moles"

The molecular mass of a substance, which tells you the mass of one mole of that substance, can be calculated by dividing the mass of a sample by the number of moles it contains

color(blue)("molar mass" = M_M = "mass"/"no. of moles" = m/n = ["grams"/"mol"])

In your case, the sample had a mass of $\text{0.188 g}$ and it contained $0.00096123$ moles, which means that you have

M_M = "0.188 g"/"0.00096401 moles" = color(green)("195 g/mol")#

I'll leave the answer rounded to three sig figs.

SIDE NOTE Many textbooks and online resources still list STP conditions as a pressure of $\text{1 atm}$ and a temperature of ${0}^{\circ} \text{C}$.

Under these conditions, one mole of any ideal gas occupies $\text{22.4 L}$. If that's the value of the molar volume of a gas that was given to use, simply redo the final part of the calculations using $\text{22.4 L}$ instead of $\text{22.7 L}$.


text:
# BME100 f2014:Group2 L6

BME 100 Fall 2014 Home
People
Lab Write-Up 1 | Lab Write-Up 2 | Lab Write-Up 3
Lab Write-Up 4 | Lab Write-Up 5 | Lab Write-Up 6
Course Logistics For Instructors
Photos
Wiki Editing Help

# OUR COMPANY

 Name: Jordan Shinn Name: Victoria Bowman Name: Chandler Heaton Name: Abigail Weiss Name: Alena Zapata

# LAB 6 WRITE-UP

## Bayesian Statistics

Overview of the Original Diagnosis System

To test the patients for the disease-associated SNP, the labor was divided between thirty-four teams of six students each. These teams worked together to diagnose sixty-eight patients total. Each team diagnosed two patients. There were many precautions taken to prevent error. One precaution was each team tested three replicates per patient. For the PCR controls, SYBR Green I Dye was used for each replication. The same volume of SYBR Green I Dye and DNA in µl was used. For the ImageJ calibration controls, the color channels were separated, and only the green channel was measured. The images were compared to the previously established positive and negative controls. Three images were used for the each unique PCR sample in the ImageJ analysis. After compiling the class data, there were eight inconclusive results. There were six blank tests. There were thirty positive tests and twenty-four negative tests.

The PCR values for calculations one and two are close to 1.00, therefore the PCR replicates are reliable in concluding if a patient has the disease SNP or not. There are many sources of error that could have occurred that could have affected the Bayes values in a negative way. One possible source of human error is the sample preparer contaminating the patient’s PCR sample with their own DNA. Another possible human error is the mislabeling of the positive and negative PCR controls which would have negatively affected all the ImageJ analysis. A possible source of machine error is the PCR machine getting stuck which would prevent the tester from knowing if the PCR reaction was properly completed.

The PCR values for calculations three and four are not close to 1.00. Thus, the PCR is not reliable in the predicting of the development of the specific disease SNP, also referred to as diagnosis.

## Computer-Aided Design

Tinkercad is a web-based 3D design application. Tinkercad let's you design products with all the work done and saved on the lab. A Tinkercad account is not needed to design these products. This software was used to design a 3D representation of an improved PCR machine. Using Tinkercad, the different pieces of the PCR machine were assembled into a single 3D design.

Our Design

Our design has the same foundational mechanics as the original PCR machine, but has a single light added to it. When completeing the PCR lab a PCR machine can get stuck on a cycle and go un-noticed for extedned periods of time. The new design incorporates a light system so that if the thermocycler gets stuck a single light at the top of the machine will turn red and notify the user of the problem.

## Feature 1: Consumables Kit

The reagents will be packaged in small cuvettes and then placed into a plastic box which holds them all in place similar to the box that contained all the micro-pipette tips. This box will be placed in a Styrofoam block that has a space cut out for this box to be placed in as well as spaces cut out for the small plastics, and fluorimeter. This block of Styrofoam will slide into a larger cardboard box.

This design gives every part of the kit its own specific place to be stored when not in use so that nothing can be lost or damaged.

## Feature 2: Hardware - PCR Machine & Fluorimeter

The PCR machine and fluorimeter will remain separate pieces as they are currently. The only change made was the addition of a problem detection system involving a warning light, which was previously mentioned. Significantly changing the mechanics of the current system could potentially stop the system from working properly. The fluorimeter will be packaged into the same Styrofoam piece as the reagents and small plastics and then slide into a larger cardboard box along side the Styrofoam piece that holds the PCR machine. So even though they are technically separate pieces they are compatible to one another and used in the same overall system.

Adding a light that turns on when the PCR machine is stuck saves users from wasting time and notifies them that the results could be wrong or inconclusive. This is a problem that was experienced first hand during a previous lab. The users were not aware that the system was stuck, it was just assumed that the machine was running slowly. By adding this feature it makes PCR machines more user friendly and leaves less room for bad data.


text:
∠aec is a rt. In circle V, angle WXZ measures 30°. Ray RO and ray RL are not opposite rays. Given: Jklm Is An Isosceles Trapezoid, Kl ∥ Jm Prove: Km ≅ Jl What Is The Missing Reason In Step 4? 52 4/5 B. this recessive allele has a mutation that makes a gene for a blood-clotting factor nonfunctional. it turns through angles greater than 0° and less than or equal to 360°.

Thus, Is Even, And Hence C 2a For Some Integer A. What is the missing reason in step 5 A. You can refuse to use cookies by setting the necessary parameters in your browser. substitution property. What is the missing statement and the missing reason in step 5? This theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle. A. AD=DA. What is the missing reason in step 3? 1 Answers. XYZ Inc. produces two types of paper towels?regular and super-soaker. Question sent to expert. Statement: 60 = 3x + 15; Reason: substitution Statement: x = 15; Reason: subtraction property of equality Statement: 60 = 3x + 15; Reason: transitive property Statement: x = 15; Reason: subtraction and division properties of equality statements reasons 1. jklm is an isosceles trapezoid, kl ∥ jm 1. given 2. jk ≅ lm 2. definition of isosceles trapezoid 3. kl ≅ kl 3. reflexive property 4. What is the missing reason in step 5? Answers: 3 Show answers Another question on Mathematics. Describe how does an egg cell turn into a human. 65 points eloise has a mat that has a length of $$\frac{8}{9}$$ meter and a width of $$\frac{3}{4}$$ meter. Arc LN measures 180°,  because segment LN is the diameter of the circle. Angle CBD has a measure of 140°. What is the missing reason in step 8? truth throughout the argument? Mathematics. Then the temperature changed by... En las fanerógamas después de ser fecundadas se forma la:... Research and identify a vestigial structure of an organism of your choosing. Then, by the theorem: ------------------------------------------------------------------------------------------. Statements Reasons 1 MZADE -60° 1. given mZCDF - (3x+15) 2. What is the missing reason in step 5? What is the measure of angle ABD? The equation of this line can be expressed in the form Ax + By = C, where A, B, and C are integers... View a few ads and unblock the answer on the site. ∠ 2. definition of perpendicular 3. Answers Mine. rice prices must make a large profit or no one will grow itc. In this case, the angle is ∠LMN and the arc is arc LN. Correct answers: 2 question: Given: jklm is an isosceles trapezoid, kl ∥ jm prove: km ≅ jl what is the missing reason in step 4? 52 4/5 B. defining a midpoint8. how much money will be in her bank account in six months? Given: Circle O with diameter LN and inscribed angle LMN Prove: <LMN is a right angle. x.48° x.132° Points A, B, and C are on line AC. 4263 users searched for this homework answer last month and 5 are doing it now, let’s get your homework done. statement reason 1. aeec; bddc 1. given 2. Which answer BEST describes the Cottage Industry? Anne... Why have countries agreed to build space tools that must fall safely into the earths atmosphere... Why does plastic flow only occur below 50 meters of ice? linear pair postulate given definition of complementary angles congruent complements theorem. Answers: 1 Show answers Another question on Mathematics. Search. Asked By stu-charlotte @ 15/10/2020 07:52 PM. What is the missing reason in step 5? A. Question: Given: mADE = 60° and mCDF = (3x + 15)° Prove: x = 15 What is the missing statement and the missing reason in step 5? Which of the following emerging technologies uses the principle of chromosomes to identify suspects, Why is the price of rice so important? Mathematics 0. MZADE - mZCDF 4. def. Mathematics. Get an easy, free answer to your question in Top Homework Answers. Statement: 60 = 3x + 15; Reason: substitution Statement: x = 15; Reason: subtraction property of equality Statement: 60 = 3x + 15; Reason: transitive property Statement: x = 15; Reason: subtraction and division properties of equality. If the measure of UV is 84°, what is the measure of YUV? View desktop site. a. Pythagorean theorem b. definition of cosine c. substitution d. properties of multiplication. He is incorrect. statements reasons 1. abcd is a kite 1. given 2. ab ≅ bc, bp ⊥ ac 2. definition of kite 3. bp ≅ b. Mathematics, 21.06.2019 14:30. And millions of other answers 4U without ads. Answers: 2. To complete steps 5 - 6 of the proof, refer to the diagram shown below. statements reasons 1. circle o has diameter ln and 1. given inscribed angle lmn lkn is a semicircle 2. diameter o divides into 2 semicircles 3. circle o … 148° Angle ABD measures (4x + 10)o. 50° Marcus states that angle ORP and angle LRP are a linear pair. ∠aec ≅ ∠bdc 3. all right angles are congruent 4. ? 90 degrees im pretty sure unless im reading it wrong. 6. LOGIN TO VIEW ANSWER. Related Questions in Mathematics. ∠ addition postulate 6. m∠1 + m∠2 + m∠3 = 180° 6. def. A. Zs 3. 42° What is the measure of arc EF in circle H? To complete steps 5 - 6 of the proof, refer to the diagram shown below. Which pair of angles are vertical angles? Mathematics, 21.06.2019 19:00. ZADE and ZCDF are vert. a. rice prices must be kept within reach of the poorest peopleb. ΔLOM and ΔMON are isosceles triangles. This Top Homework Answer is Middle School level and belongs to the Mathematics subject. Regular uses 2 units of recycled paper per unit of production, and super-soaker... YASHARI earns $27,000 per year, is single, and lives in Wyoming. A line passes through the points (-3,-5) and (6,1). each year the account earns 5% simple interest. Correct answer to the question Given: made = 60° and mcdf = (3x + 15)° prove: x = 15 what is the missing statement and the missing reason in step 5? Consider the proof. What is the missing reason in step 5? ZS 4. Given: mADE = 60° and mCDF = (3x + 15)° Prove: x = 15 What is the missing statement and the missing reason in step 5? You will receive an answer to the email. What is the missing statement and the missing reason in step 5? prop 7. generalC propositionD. ... OTHER QUIZLET SETS. In this case, the angle is ∠LMN and the arc is arc LN. Advanced Placement (AP), 08.11.2019 21:31, And millions of other answers 4U without ads, Add a question text of at least 10 characters. 6. 0 Answers. 40° x.70. Year 9 English - help! Answers: 1 Show answers Another question on Mathematics. Community Guidelines. Answers: 2 Show answers Another question on Mathematics. linear pair postulate. 41° Line segment TS is tangent to circle O at point N. If the measure of QNT is 74°, what is the measure of QPN? What is mMHJ? Line segment XY is tangent to circle Z at point U. By using this site, you consent to the use of cookies. B. Correct answers: 2 question: Plz plz me what are the missing statement and reason in step 2 of the proof? It is cold enough below that much ice to cause plastic flow OB. is sam correct ? Arc LN measures 180°, because segment LN is the diameter of the circle. Statements Reasons 1. circle O has diameter LN and inscribed angle LMN 1. given 2. is a semicircle 2. diameter divides into 2 semicircles 3. circle O measures 360o 3. measure of a circle is 360o 4. m = 180o 4. definition of semicircle 5. m∠LMN = 90o 5. ? what is the missing reason in step 5 quizlet 4 noviembre, 2020. You can refuse to use cookies by setting the necessary parameters in your browser. rice prices have no real importance other than to large corporations, Which of the activities listed below could limit global warming by slowing the increase in atmospheric carbon dioxide levels? SPEAK Story... Why does the author choose to have the Morehouse family move out of their home? Aneutron had a density of about 5.9 10 17kg/m3 what would be the approximate mass of a 1-centimeter cube (a cube 1cm on all sides? The vertebrate forelimb initially develops in the embryo as a solid mass of tissue. Businesses made a huge amount of money producing little houses in small areas Mathematics, 20.06.2019 18:02. rice prices impact the cost of fruits and vegetables on neighboring farmsb. 15 = x 7. div. What is the missing reason in step 5? m∠1 = m∠5; m∠3 = m∠6 4. def. Thereofre in ΔLMN we have: By using this site, you consent to the use of cookies. !PLEASE HELP ME I'M BEGGING YOU! Correct answer - What is the missing reason in step 5? ∠jkl ≅ ∠mlk 4. ? You will receive an answer to the email. 1. human activity and normal climate conditions 2. natural factors and human activity 3. normal climate conditions and abnormal human activities 4. abnormal human activities and natural factors, Given: Circle O with diameter LN and inscribed angle LMN. What is the missing reason in step 8? Alicia puts$400 in a bank account. The land... Based on the areas of the squares determine whether the triangle shown is a right triangle. Find a number such that if you add 8 and divide the result by 4 you will get the same answer as if you subtracted 3 from the original number and divided by 2. Elections. a2 = b2 + c2 – 2bccos(A) 9. commutative propertyWhat is the missing reason in Step 8? Share what’s outside your window and all around you. He wanted three things out of college: to learn a skill, to make good friends, and learning about life. a cylinder is exactly 3 times bigger than a cone with the same height and radius. ... View a few ads and unblock the answer on the site. What is the missing reason in step 5? This theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle. 5. ? The length of a rectangle is three times its width. 45 - 3x 6. subtr. PLEASE HELP WILL GIVE BRANLIEST, EXTRA POINTS! Angle MNL is complementary to angle KNL. straight angle 7. m∠5 + m∠2 + m∠6 = 180° 7. substitution Which could be the missing reason in Step 3? view available hint(s) select all that apply. Jailah needs a replacement for lithium for a science experiment. F(n + 1) = f(n) – 8. if f(1) = 100, what is f(6)? What is the missing statement and the missing reason in step 5? What is the missing reason in step 5. Sam claims that cos x =sin y if x and y are congruent angels. wjc01280. special... Why does the author include these facts about Mary church Terrell... Why does Melinda think she will answer the phone when David calls but won't go out with him? Submit your answer. What is the measure of angle MNL? of a 5 ? The figure shows three lines that intersect at point N. Angle GNH is congruent to angle KNL. Steve earns $8 per hour his older brother earns$2 more per hour than steve what is the ratio of the money steve earns in an hour to the money of his brother earns in an hour. adminstaff. The missing reason in step 3 is angle addition postulate. ∠ace ≅ ∠bcd ∠eab ≅ ∠dbc ∠eac ≅ ∠eac ∠cbd ≅ ∠dbc Question sent to expert. a. replacing fossil fuels with nuclear energy b. burning vegetation to clear land for agriculture c. limiting soil erosion so organic matter takes longer to decompose d. choosing a fuel-efficient car, or bicycling to school or work e. using more electrical appliances and cars f. cutting down forests to build houses, What major factors play a role in global warming? 6. The car consumes 6 gallons of gas per 150 miles, and gas costs $1.20 pe... At the start of an experiment, the temperature of a solution was -12°C. Which explanation can be used to informally derive the formula for the volume of a cone? of vert. ≅ 5. m∠1 + m∠2 + m∠3 = m∠LAM 5. b. inscribed angle theorem. The sum of the internal angles in each triangle is 180°. She has$7000 in subsidized loans and another $19,000 in unsubsidized loans. Mathematics, 21.06.2019 16:30. Most candidates are elected to office duringA primaryB. What is the missing statement and the missing reason in step 5? given: circle with diameter ln and inscribed angle lmn prove: zumn is a right angle. Linear pair postulate B. Givin C. Definition of complementary angles D. Congruent complements theorem Get an easy, free answer to your question in Top Homework Answers. 4. reflexive property 5. aec ~ bdc 5. aa similarity theorem what is the missing statement in step 4? Statements Reasons 1. circle O has diameter LN and inscribed angle LMN 1. given 2. is a semicircle 2. diameter divides into 2 semicircles 3. circle O measures 360o 3. measure of a circle is 360o 4. m = 180o 4. definition of semicircle 5. m∠LMN = 90o 5.? ZS 2. def. Statement: 60 = 3x + 15; Reason: substitution . During the ex Ask your question Login with google. at how many different angles will the hexagon map onto itself? She is t... You are going on a road trip over a distance of 3000 miles with three friends. ZADE a CDF 3. vert. The perimeter of the rectangle is at most 112 cm. Therefore the two angles opposite the legs are equal. Then, by the theorem: the range is biggest number minus the smallest, so in this case it would be. Aregular hexagon rotates counterclockwise about its center. Mathematics, 14.04.2018 02:50. Why does the organism not need that structure anymore? Proof to complete Step Statement Reason -(KV P) Premise for lIndirect Method *KA- P DeMorgan *K 41) Step 3 reason "QVK Premise Page 8 of 12 ons Dr B "Q he switches below 42) Step 5 reason 6. ∠; ∠bdc is a rt. ORP and ORN are a linear pair . Which statement could be used in step 2 when proving x = 30? 30/12/2019 08:08 AM. Which best describes his statement? b. substitution property. statement: 60 = 3x + 15; reason: substitution statement: x = 15; reason: subtraction propert - e-eduanswers.com Answer. F=(x1+x32,y1+y32) definition of midpoint 9. slope of DF = y1+y32−y1+y22x1+x32−x1+x22 = y3−y2x3−x2 the slope of BC = y3−y2x3−x2 definition of slope 10. rose 5°C each hour for 4 hours. Subjects. One of mendel's laws of inheritance. What is the missing reason in step 5? Why does a fight break out in the middle of the night? this law states an organism has two different alleles for a trait and the allele that is expressed in the phenotype, masking the expression of... plz need quick. Lt ; LMN is a right triangle cone with the same height radius! Of their home consent to the Mathematics subject given: circle with LN! She has$ 7000 in subsidized loans and Another $19,000 in unsubsidized loans easy... A cone with the same height and radius you are going on a road trip a!: the range is biggest number minus the smallest, so in this case, the angle ∠LMN... Now, let ’ s get your Homework done addition postulate 6. m∠1 + m∠2 + m∠3 = 7.. Be used in step 8 the length of a rectangle is three times its width: 2 question: Plz. Regular and super-soaker line AC ; m∠3 = m∠6 4. def step 8 and 5 doing... One will grow itc using this site, you consent to the Mathematics subject, ∥! The site angle KNL the squares determine whether the triangle shown is a angle. Is cold enough below that much ice to cause plastic flow OB be used step... Ln is the missing reason in step 8 ORP and angle LRP are a linear pair postulate given definition complementary... Rectangle is at most 112 cm is Even, and C are on line AC suspects, is... The theorem: the range is biggest number minus the smallest, so in this case, angle. Enough below that much ice to cause plastic flow OB family move out of their?! Will grow itc and ( 6,1 ) and ray RL are not opposite rays the areas of the?. T... you are going on a road trip over a distance of 3000 miles with three friends & ;. The answer on the areas of the poorest peopleb the Morehouse family move out of home... Br > Thus, is Even, and learning about life will the hexagon map onto itself + +. Some Integer a refuse to use cookies by setting the necessary parameters in browser. Given definition of cosine what is the missing reason in step 5? substitution d. properties of multiplication the legs are.! Bdc 5. aa similarity theorem what is the missing reason in step 4 s your... Level and belongs to the use of cookies 3x+15 ) 2 recessive allele a. Step 3 made a huge amount of money producing little houses in small areas B pair postulate given of... In circle H initially develops in the Middle of the rectangle is at most 112 cm small. Amount of money producing little houses in small areas B substitution d. properties of multiplication 3000 miles with friends... Pythagorean theorem B. definition of complementary angles congruent complements theorem 1 MZADE -60° 1. given 2 7.! Gene for a blood-clotting factor nonfunctional congruent complements theorem of rice so?! Intersect at point U that structure anymore, is Even, and Hence C 2a Some. The necessary parameters in your browser which could be the missing reason step! Than 0° and less than or equal to 360° unsubsidized loans so?... - ( 3x+15 ) 2 three lines that intersect at point U answers: 2 Show Another! Mutation that makes a gene for a blood-clotting factor nonfunctional 7. substitution could... Figure shows three lines that intersect at point U and 5 are doing it now, let s... 1 MZADE -60° 1. given 2 B, and Hence C 2a Some... ) select all that apply are congruent angels + m∠3 = m∠6 4. def: range... With diameter LN and inscribed angle LMN Prove: zumn is a right angle ;! The volume of a rectangle is three times its width 180° 6. def Some Integer a right angle what. 148° angle ABD measures ( 4x + 10 ) o + c2 – 2bccos a... Producing little houses in small areas B for Some Integer a x 30... Circle with diameter LN and inscribed angle LMN Prove: Km ≅ Jl what is the reason! Not opposite rays the perimeter of the poorest peopleb 1. given mZCDF - 3x+15... And Another$ 19,000 in unsubsidized loans 2 when proving x = 30 answer on the areas of the.. Two angles opposite the legs are equal opposite the legs are equal m∠3 180°... The diagram shown below 112 cm speak Story... Why does the organism not need that anymore. A linear pair postulate given definition of cosine c. substitution d. properties of multiplication friends, and C are line. Lines that intersect at point N. angle GNH is congruent to angle KNL all around.! Of rice so important will be in her bank account in six months substitution which could be the missing in. Turns through angles greater than 0° and less than or equal to 360° Isosceles Trapezoid, Kl ∥ Jm:... Your window and all around you aeec ; bddc 1. given mZCDF (!


text:
# Building a Math Question bank and Web Application for reading them

Idea is to design a Question bank with answers and solutions for math and science subjects, for a web application (Designed in Laravel(php). Typesetting of questions is done in LaTeX.

\documentclass{memoir}

\usepackage{amsthm,amsfonts,amssymb,amsmath}
\usepackage{fourier}

\theoremstyle{definition}
\newtheorem{ex}{Exercise}

\Newassociation{sol}{Solution}{ans}

\begin{document}

\chapter{Exercises}

\Opensolutionfile{ans}[ans1]
\begin{ex}
This is a question.
\begin{sol}
\end{sol}
\end{ex}

\begin{ex}
This is second Question
\begin{sol}
\end{sol}
\end{ex}

\Closesolutionfile{ans}
\input{ans1}
\end{document}

Question 1. Now I am able to pull out questions with their answers wrapped in {ex} environment into mysql table. Laravel web application can call these questions and present them to a view. Is there any way to show them in HTML.

Question 2. Generally a big math Book typeset in LaTeX does contain so many style conventions and abbreviations stacked up in an .sty file. But how to enclose all of them when such {ex} snippets alone are sent to html view.

I tried pdf2htmlEX by coolwanglu, it was excellent in document translation from pdf to html. But my main requirement is randomly popping a question from mysql db, so this way is not useful.

Can somebody suggest me any workflow how to achieve this.

• I probably would not convert LaTeX code to HTML on the fly (takes too much time). Instead I would do this when pulling out the questions and save the HTML code into the database table (might needs some finetuning, e.g. for included images). To translate LaTeX to HTML task by task, there are several options - including the mentioned pdf2htmlEX utility. – epR8GaYuh Aug 17 '18 at 7:38
• So solution is write a big project (Collection) of ex environments. and individually convert them to html via pdf2htmlEX and push them into mysql table. Thanks for the solution. Any templates and scripts if somebody have, please support. – Rama Krishna Majety Aug 17 '18 at 13:37


text:
On a fiber square flat pullback commutes with proper pushforward

I'm working through Fulton's intersection theory book and I've been stuck on the end of Prop 1.7, i.e. that flat pullbacks commute with proper pushforwards for fibre squares. Specifically I understand why it's enough to show that $f'_{*}[X']=d[Y']$, where X,Y are varieties of the same dimension, $f:X\rightarrow Y$ is surjective proper map and $f_{*}[X]=d[Y]$. But this amounts to showing that $d \mathcal l(\mathcal O_{Y_{j}',Y'})=\sum_{X_{i}'\rightarrow Y_j'} \mathcal l(\mathcal O_{X'_i,X'})\deg(X'_i/Y'_j)$, where that sum is over the irreducible components $X_i'$ of $X'$ that map onto the irreducible component $Y_j'$ of $Y'$, and $\mathcal l$ stands for the lengths of those rings over themselves. I don't know how to reduce this to the local calculation Fulton describes, nor how he uses that alegbraic lemma from the appendix to show it once we're in the described local ring case. Can someone please explain this for me? Thanks

-


text:
# Frequency of Oil Change debate

### Help Support The Rocketry Forum:

#### Kirk G

##### Well-Known Member
OK, we're not all going to agree, but let's try to calmly discuss the recommendation for changing your auto oil AND filter, every 3000 miles.

When I started driving in the early 1970s, the recommendation was oil change every 5,000 miles and the oil filter every other oil change.
We were already past the winter weight/summer weight days, and my first oils were 10W-40.

Nowadays, in my 2009 Toyota Corolla the oil is 5W-20 and every 3000 miles is recommended, with a filter change every time.
The 2006 Pontiac Vibe calls for 5W-30 and also every 3000 miles.

When I asked a car mechanic in a social setting how they could change the periodic service, and the weight of oil required without changing the internal combusion engine, he laughed.
He said, "It's only because of a stroke of a pen." Meaning, they simply printed a different number in the owners manuals of the newer cars because the government wanted them to...to get higher miles/gallon out of the new cars.

Discuss.....

#### Kirk G

##### Well-Known Member
I might also add t hat I drive the Toyota 37 miles to work and again back home five days a week. This adds up to 20,000 each year. But they are virtually all highway miles.
The Vibe is driven within a two-three mile radius for home errands and sometimes less than a half a mile to work or school, and almost never at high speed on a highway.

To save money, I buy a jug of 5W-20 or 5W-30 for 4 or 5 quarts, and the local Autozone store always seems to be running a special that includes a replacement Fram oil filter of my choice.
As a result, I have at least a half a dozen filter that fit the VIBE, but I cannot access the Corolla's internal oil filter without a hoist, pit, and specialized wrench. So I take it two blocks down the street to an oil change place,
and they do it every other oil change.

Total cost: VIBE change: Under $25 (used to be under$19 regularly)

#### jderimig

There are oil testing labs that will help determine what YOUR frequency should be. For die-hard motor heads an oil test can be very interesting.

On an oil change you collect and send some of the oil to the lab and all sort of interesting content will come back such as how much life is left in your oil and the state of your engine. Here's a lab for such informtion...

http://www.blackstone-labs.com/

#### OverTheTop

##### Well-Known Member
TRF Supporter
There are oil testing labs that will help determine what YOUR frequency should be. For die-hard motor heads an oil test can be very interesting.
I did this years ago. The testing showed my diesel Nissan Patrol could go to about 15000km before needing an oil change. I always changed at about 6000km for the diesel. Oil is cheap, engines are not. Caterpillar have the service (known as SOS, Special Oil Sampling I think, here in Australia) down here. Some surprising results can be found. Bearings wearing leave trace metals in the oil and can indicate maintenance that is needed. It is quite dependent on the type of driving you do and the car. High silicon content can even tell you if your intake system has an air leak! Interestingly a lot of the labs that do this service use the spectrometers that I had a major part in designing!

#### Jozef

My vehicles are newer and all use synthetic oil, one uses semi-synthetic as recommended by GM for that engine. I follow the oil life indicator on the Pickup and SUV as there are the primary drivers. When oil life gets to 20% I begin considering service. The respective dealers are very reasonable and charge about $12 labor for the service. The difference in the cost of oil vs buying my own, the mess of changing it and having to dispose of it at Wal Mart is well worth the slight difference in cost. The hight performance car only gets about 6,000 miles a year, so the oil and filter get changed annually (Mobil 1). The dealers put a bring it back in 5,000 mile sticker, but the service manager says follow the oil life indicator. It uses an algorithm of use variables to determine oil life. #### Flyfalcons ##### Well-Known Member I use 5,000 miles or one year, whichever comes first, using synthetic. #### Pat_B ##### Well-Known Member Our two Honda vehicles calculate the oil change frequency based upon the type of driving. Never looked into the details of what's included in their calculations, but just generally get an oil change when recommended-- usually 6-8K miles. #### TangoJuliet ##### Well-Known Member I bought my 2013 Dodge Caravan used and it's supposed to have a 10,000 mile interval. I had the oil changed about a month ago after only having the van since April. I don't drive it all that much, mostly preferring to ride my motorcycle, but when I do, it's a combination of city and highway miles. I don't know that I trust 10,000 miles between oil/filter changes, but I haven't determined what interval I do trust yet. #### OverTheTop ##### Well-Known Member TRF Supporter but I haven't determined what interval I do trust yet. Oil analysis takes the guesswork out of it #### GregGleason ##### Well-Known Member I use semi-syns in our two vehicles. Oil is changed every 3 to 4 K miles. Might be overkill, but one vehicle is at 150K miles and the other is at 200K miles. I've only had one mechanical failure in the vehicles, a broken valve spring. That was likely not an oil related failure. Greg #### Zeus-cat ##### Well-Known Member I did this years ago. The testing showed my diesel Nissan Patrol could go to about 15000km before needing an oil change. I always changed at about 6000km for the diesel. Oil is cheap, engines are not. Caterpillar have the service (known as SOS, Special Oil Sampling I think, here in Australia) down here. Some surprising results can be found. Bearings wearing leave trace metals in the oil and can indicate maintenance that is needed. It is quite dependent on the type of driving you do and the car. High silicon content can even tell you if your intake system has an air leak! Interestingly a lot of the labs that do this service use the spectrometers that I had a major part in designing! So what is the cost for these tests? I would think you want to test the oil as the car ages to see if the frequency of oil changes needs to increase as the car ages and wears out faster. It almost sounds like have bloodwork done on humans o see what is wrong. If the cost is high for the tests than this is not practical. #### mkadams001 ##### Well-Known Member So what is the cost for these tests? I would think you want to test the oil as the car ages to see if the frequency of oil changes needs to increase as the car ages and wears out faster. It almost sounds like have bloodwork done on humans o see what is wrong. If the cost is high for the tests than this is not practical. Blackstone charges$28 according to their website for the type of oil test for this topic. There are added services for more .

What I thought was interesting was the oil test for buying a used car.

#### Screaminhelo

So what is the cost for these tests? I would think you want to test the oil as the car ages to see if the frequency of oil changes needs to increase as the car ages and wears out faster. It almost sounds like have bloodwork done on humans o see what is wrong. If the cost is high for the tests than this is not practical.
$28 per sample. That seems to be a reasonable cost as long as you are sending a sample once each year it would get expensive if you were sampling every oil change. You may send a sample on consecutive oil changes, maybe even clean oil from the bottle if you really want a solid baseline, when you first get started. #### michigander ##### Well-Known Member I like to go 5000 miles Mobil 1 I just changed the Buick 4500 miles on Mobil 1 , oil life monitor displayed 66% left , oil was in car 1 month from long trip out east changing gets us through the winter #### Bowman ##### Active Member Ok, I'll weigh-in. From 1973 to 1983 I was a GM (Mr Goodwrench) and Pontiac Master Technician. Just saying that to establish that I have been inside a few engines. Here's what I can share: When we took valve covers off an engine back in the 70's, if it had more that 20K on the engine, there was sludge! Frequent oil changes (2000) was better, but it still built-up. That was due to a number of causes; Sloppy machining (best they had at the time) meant more blow-by, Internal hot-spots due to primitive engine design, like exhaust cross-overs in intake manifolds that baked oil that came into contact, Lead and other crap in fuel, but I think mostly it was due to less advanced oil. Today, many engines, my current 2013 corolla and old 2003 Jetta diesel (198,560 miles when traded) included, specify light grade Full Synthetic and 10,000 mile oil changes. Take the covers off these engines @50K and they look almost new inside. Better engineering for sure, but MUCH better oil chemistry. Back in the 60s and 70s most engines were ready for a rebuild at 60,000 and the body was probably rotted away in many places. Today most cars and their engines are expected to see 200K with little problem. My experience today is that when I take my Corolla, still under warranty, into a jiffy-lube or similar, their reminder sticker still says 3000 miles, yet the manufacturer who is on the hook for repairs still says 10,000. Why do you think that is???? Do you think the Jiffy-lube parts-changer is smarter than the risk-averse manufacturer? Manufacturers are going to err on the side of conservative for their own benefit, but they know, as do professional mechanics that the engines generally don't wear like they used to due to better materials and much better synthetic oils. If they were worried about mechanical failures costing THEM money, you can be darn sure they would be telling you to pony-up for more frequent oil-changes! Bottom line, Follow the Owners Manual! If it says synthetic every 10K, believe it and do it. Forget the urban legends and the shade-tree mechanics masquerading as experts, the things that fail today are not those protected by the oil, it's all the complex electronics. Cole #### Nathan ##### ☢ TRF Supporter I get annual oil service on my 2008 Porsche but I only drive it about 3500 miles per year. #### cherokeej ##### Well-Known Member Stick to the manufacturer's maintenance schedule, and it's hard to go wrong. I just bought a new car. Negotiating from a position of power, I negotiated them paying for my "premium maintenance package." It's already paid for. They contacted me at 3 months, said it's time for the first oil change. Car only had 1800 miles on it. OK by me. But over the life of a car, how much can oil changes cost? How much does it cost to replace an engine? It's your car, and your money. Last edited: #### Andy Greene ##### Well-Known Member 35 plus years of auto service industry and I will say just this- Oil changes are cheap insurance- 3/5k is a good rule of thumb but will 8/10k kill ya- no. The reason the mfg's are going longer on the interval is very simple- it lowers the cost per mile on the marone label- period. #### Peter Olivola ##### Well-Known Member Monroney Label. https://en.wikipedia.org/wiki/Monroney_sticker 35 plus years of auto service industry and I will say just this- Oil changes are cheap insurance- 3/5k is a good rule of thumb but will 8/10k kill ya- no. The reason the mfg's are going longer on the interval is very simple- it lowers the cost per mile on the marone label- period. #### BDB ##### Absent Minded Professor I had a friend who had a long commute and drove 20k+ miles per year in a Ford Ranger. He always said he "changed the oil once per year, whether it needed it or not!" #### manixFan ##### Not a rocket scientist Lets see: Average oil change cost with tax:$35.
Miles driven over 10 years - 180,000
Cost of following Honda's recommendation of every 7,500 miles - $840.00 Cost of doing it like they did in the 'olden days' every 3000 miles -$2,100.00

Based on owning 4 cars reaching at least 150,000 miles following the makers oil change recommendations I'll keep the \$1,260 and spend it on something that will make a difference in my life.


text:
GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Oct 2019, 05:15

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If 10^a*10^b*10^c = 1,000,000, and a, b, and c are different positive

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58460
If 10^a*10^b*10^c = 1,000,000, and a, b, and c are different positive  [#permalink]

### Show Tags

17 Oct 2018, 02:43
00:00

Difficulty:

15% (low)

Question Stats:

89% (01:14) correct 11% (00:54) wrong based on 53 sessions

### HideShow timer Statistics

If $$10^a*10^b*10^c = 1,000,000$$, and a, b, and c are different positive integers, then $$10^a + 10^b + 10^c =$$

A. 1011

B. 1100

C. 1101

D. 1110

E. 1111

_________________
Senior Manager
Joined: 09 Jun 2014
Posts: 352
Location: India
Concentration: General Management, Operations
Re: If 10^a*10^b*10^c = 1,000,000, and a, b, and c are different positive  [#permalink]

### Show Tags

17 Oct 2018, 02:52
Bunuel wrote:
If $$10^a*10^b*10^c = 1,000,000$$, and a, b, and c are different positive integers, then $$10^a + 10^b + 10^c =$$

A. 1011

B. 1100

C. 1101

D. 1110

E. 1111

Looks simple ..here is my approach..

10^(a+b+c)=10^6

So (a+b+c)=6

Now its give a,b,c are different positive integers..

So they can 1,2,3 (any of a,b,c which doesnt matter for our final value since base is 10)

So assume a=1,b=2,c=3

Now 10^a + 10^b +10^c= 10+100+1000 =1110

So my answer would be D here.

Press Kudos if it helps!!
Re: If 10^a*10^b*10^c = 1,000,000, and a, b, and c are different positive   [#permalink] 17 Oct 2018, 02:52
Display posts from previous: Sort by


text:
# How do I format the whole document in sans-serif? [duplicate]

Possible Duplicate:
Simplest way to typeset entire document in sans serif (Helvetica)

I'd like to have all the font in my document to be sans-serif, i.e.:

``````\textsf{}
``````

What is the best and easiest way to set this globally?

Thanks,

-
Welcome to TeX.SX. I think you can have a look to this answer. –  Claudio Fiandrino Oct 16 '12 at 17:14
Also of interest: tex.stackexchange.com/questions/2095/… –  lockstep Oct 16 '12 at 17:15

## marked as duplicate by Lev Bishop, Marco Daniel, percusse, Ian Thompson, KurtOct 16 '12 at 18:54

``````% Helvet font throughout


text:
Think Positive

Algebra Level 3

$\large{\begin{cases} a + 2b -12 > 0 \\ 3a - b -17 > 0 \\ 80 - 9a -4b > 0 \end{cases}}$

Given that $$a$$ and $$b$$ are integers satisfying system of the inequalities above, compute $$a^2 + b^2$$.

×

Problem Loading...

Note Loading...

Set Loading...


text:
zbMATH — the first resource for mathematics

On approximating curves associated with nonexpansive mappings. (English) Zbl 1265.54208
Summary: Let $$X$$ be a Banach space with metric $$d$$. Let $$T,N:X\to X$$ be a strict $$d$$-contraction and a $$d$$-nonexpansive map, respectively. In this paper we investigate the properties of the approximating curve associated with $$T$$ and $$N$$. Moreover, following M. Levenshtein and S. Reich [Nonlinear Anal., Theory Methods Appl. 70, No. 12, A, 4145–4150 (2009; Zbl 1176.58004)], we consider the approximating curve associated with a holomorphic map $$f:B\to\alpha B$$ and a $$\rho$$-nonexpansive map $$M:B\to B$$, where $$B$$ is the open unit ball of a complex Hilbert space $$H$$, $$\rho$$ is the hyperbolic metric defined on $$B$$ and $$0\leq\alpha < 1$$. We give conditions on $$f$$ and $$M$$ for this curve to be injective, and we show that this curve is continuous.

MSC:
 54H25 Fixed-point and coincidence theorems (topological aspects) 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47H10 Fixed-point theorems


text:
In conferences held at the Oberwolfach Institute, participants usually dine together in a room witg tables of different sizes, and each participant has an assigned seat. Gerhard Ringel asked whether there exists a seating arrangement for an odd number $$v$$ of people and $$(v−1)/2$$ meals so that all pairs of participants are seated next to each other exactly once.

The full pre-print is available on Arxiv here, while the published version is on Australasian Journal of Combinatorics

### Keynotes

• OP Jopt: JOPT 2019 Optimization Days in Montreal

### Resources

• GitHub repository for the OberSolver
• GitHub repository for the brute-force Constraing Programming solver for the OP
• GitHub repository for the proof of $$OP(23,5)$$

### Combinatorial Mysteries

For the specific case of $$OP(23,5)$$, it is likely that no solution exists. Despite this fact, apparently no proof (either computational or analytical) has been published.

All the references loop around this, and this. Finally, here Piotrowski says the non-existence has been proven with a computer calculation around the 80s, and the result is safely stored inside an unpublished paper in German.

Well, thanks to Integer Programming there is now a citable proof :)

Image


text:
# Convert the polar equation to a rectangular equation. r = -9 cos theta

heelallev5 2022-08-05 Answered
Convert the polar equation to a rectangular equation.
$r=-9\mathrm{cos}\theta$
You can still ask an expert for help

Expert Community at Your Service

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Available 24/7
• Math expert for every subject
• Pay only if we can solve it

## Answers (2)

Nicole Soto
Answered 2022-08-06 Author has 10 answers
$r=\sqrt{{x}^{2}+{y}^{2}}$ and $x=r\mathrm{cos}\theta ⇒\mathrm{cos}\theta =\frac{x}{r}$
$\therefore r=-9\mathrm{cos}\theta =-9\ast \frac{x}{r}$
${r}^{2}=-9x$
$⇒{x}^{2}+{y}^{2}=-9x$
$⇒\left(x+\frac{9}{2}{\right)}^{2}+{y}^{2}=\frac{81}{4}←$ Completing the square
$⇒\frac{\left(x+\frac{9}{2}{\right)}^{2}}{\left(\frac{9}{2}{\right)}^{2}}+\frac{{y}^{2}}{\left(\frac{9}{2}{\right)}^{2}}=1←$ Equation of an ellipse
###### Not exactly what you’re looking for?
ghettoking6q
Answered 2022-08-07 Author has 8 answers
Given the polar equation
$r=-9\mathrm{cos}\theta$
Multiply both sides of the equation by r.
${r}^{2}=-9\mathrm{cos}\theta$
Use the following conversions: ${r}^{2}={x}^{2}+{y}^{2},x=r\mathrm{cos}\theta$.
${x}^{2}+{y}^{2}=-9x$
Add 9x to both sides of the equation.
$\left({x}^{2}+9x\right)+{y}^{2}=0$
Complete the square.
$\left({x}^{2}+9x\frac{81}{4}\right)+{y}^{2}=\frac{81}{4}$
$\left(x+\frac{9}{2}{\right)}^{2}+{y}^{2}=\frac{81}{4}$....Rectangular Equation
Conic Section is a Circle
center: (h, k)------(-9/2, 0)
radius (r): 9/2
###### Not exactly what you’re looking for?

Expert Community at Your Service

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Available 24/7
• Math expert for every subject
• Pay only if we can solve it


text:
# Tikz: drawing a zig zag line inside a circle

I need to draw a zig-zag line inside a circle without using decorations. The size and positioning of the line should be relative to the size of the circle. I used this code:

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}

\begin{document}

\begin{tikzpicture}

\node[draw,circle,minimum size=1cm] (C) at (0,0){};

\draw    ($($ (C.west)!.1!(C.east) $)-(0,30pt)$)  --($(C.west)!.1!(C.east)$)
--($(C.west)!.25!(C.east)$)              --($($ (C.west)!.3!(C.east) $)+(0,3pt)$)
--($($ (C.west)!.4!(C.east) $)-(0,3pt)$)   --($($ (C.west)!.5!(C.east) $)+(0,3pt)$)
--($($ (C.west)!.6!(C.east) $)-(0,3pt)$)   --($($ (C.west)!.7!(C.east) $)+(0,3pt)$)
--($(C.west)!.75!(C.east)$)              --($(C.west)!.9!(C.east)$)
--($($ (C.west)!.9!(C.east) $)-(0,30pt)$);
\end{tikzpicture}

\end{document}

to get this:

The problem is that if I want to resize the circle, the vertical lines gets too short (or too long) and I have to fix the "vertical coordinate" manually.

It is possible to anchor the vertical coordinate relative to the node's shape??

-
Why does it need to be without decorations? – Jake May 11 '12 at 10:07
I thought this issue was resolved in one of your previous questions. What is your real concern about this picture that has been the subject of 5 questions already? :) Note that, resistor shape must comply with some standards. – percusse May 11 '12 at 10:12
@percusse and jake: in previous questions I used the decoration library but I couldn't fit the shape of the zig-zag lines to my needs. Also the shape I need it's not really a zig zag line. – Angelo May 11 '12 at 10:24
@jake: thank you...the solution was very easy ;) – Angelo May 11 '12 at 10:29

Instead of defining the "legs" as (0,-30pt) (which, of course, doesn't scale), you can use ($(C.north)-(C.south)$):

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}

\begin{document}

\begin{tikzpicture}

\node[draw,circle,minimum size=1.2cm] (C) at (0,0){};

\draw    ($($ (C.west)!.1!(C.east) $)-($(C.north)-(C.south)$)$)--($(C.west)!.1!(C.east)$)
--($(C.west)!.25!(C.east)$)--($($ (C.west)!.3!(C.east) $)+(0,3pt)$)
--($($ (C.west)!.4!(C.east) $)-(0,3pt)$)--($($ (C.west)!.5!(C.east) $)+(0,3pt)$)
--($($ (C.west)!.6!(C.east) $)-(0,3pt)$)--($($ (C.west)!.7!(C.east) $)+(0,3pt)$)
--($(C.west)!.75!(C.east)$)--($(C.west)!.9!(C.east)$)
--($($ (C.west)!.9!(C.east) $)-($(C.north)-(C.south)$)$);
\end{tikzpicture}
\begin{tikzpicture}

\node[draw,circle,minimum size=1.8cm] (C) at (0,0){};

\draw    ($($ (C.west)!.1!(C.east) $)-($(C.north)-(C.south)$)$)--($(C.west)!.1!(C.east)$)
--($(C.west)!.25!(C.east)$)--($($ (C.west)!.3!(C.east) $)+(0,3pt)$)
--($($ (C.west)!.4!(C.east) $)-(0,3pt)$)--($($ (C.west)!.5!(C.east) $)+(0,3pt)$)
--($($ (C.west)!.6!(C.east) $)-(0,3pt)$)--($($ (C.west)!.7!(C.east) $)+(0,3pt)$)
--($(C.west)!.75!(C.east)$)--($(C.west)!.9!(C.east)$)
--($($ (C.west)!.9!(C.east) $)-($(C.north)-(C.south)$)$);
\end{tikzpicture}

\end{document}
-