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A regular 7-sided polygon can be thought of as being made of 7 isosceles triangles.  Each triangle has an apex angle theta = 2pi/7.  The height is h = 2.5 and half the base length is b = h*tan(theta/2).  Hence the overall area of the polygon is:

A = 7*b*h   or  A = 7*2.5*tan(pi/7)*2.5  or  A ≈ 21.07

Not sure what you are asking, but maybe this?

t= 2 pi (w/gf)^2      solve for ' f '

t/(2pi)  = (w/gf)^2

sqrt (t/(2pi))  = w/gf

f = w/ ( g sqrt(t/(2pi)) )       Is that what you wanted?

it seems to b ur home work problem..  ill just say the method. for ques (a) just differentiate displacement equation for velocity and double differentiate for acceleration. for ques (b) substitute velocity=0 in velocity eqn. found in previous ques. for ques (c) subs the time found in (b) in eqn. of velocity n acc. in (a).

5.0-9532322653354643

5.0-9532322653354643 = -9532322653354638

What about it?

I already answered this somewhere else this morning.  ://

The interest rate is 10% compounded quarterly. You use this common TVM formula to find the rate:

FV=PV[1 + R]^N

43,257.41=6,000[1+R/4]^(20*4) you would use logs to find the interest rate.

R=2.50% per quarter x 4 =10% comp. quarterly.

Hi BlueFire28, it is nice to meet you :)

I can't figure out this one

Find the Indicated sum

the exponet is soppose to be i-1 

Thank you for your help!! 

\(\sum_{i=1}^\infty\;\left(\frac{-2}{5}\right)^{i-1}\\~\\ 1+\frac{-2}{5}+\frac{4}{25}+ \ldots\\ \mbox{This is the sum of a GP and it has a limit since r=-2/5 and |r|<1}\\ S_{\infty}=\frac{a}{1-r}=\frac{1}{1-\;-0.4}=\frac{1}{1.4}=\frac{5}{7}\\ so\\ \sum_{i=1}^\infty\;\left(\frac{-2}{5}\right)^{i-1}=\frac{5}{7}\\~\\ \)

a)Which of the residues   \( 0, 1, 2, \ldots, 11\)

satisfy the congruence \(3x \equiv 0 \pmod{12}?\)

Give your answer as a list, separated by commas, in order from least to greatest.

I am not sure what you mean by reidues??

\(3x \equiv 0 \pmod{12}?\)

Only x=0 and x= multiples of 4 would make this true.  So x=0,4,8

b)Which of the residues $0, 1, 2, 3, 4$ satisfy the congruence     \(x^5 \equiv x \pmod{5}? \)$Give your answer as a list, separated by commas, in order from least to greatest.

0^0=0  satisfies

1^5=1  satisfies

2^5=32=2 mod5    satisfies

3^5=243= 3mod5    satisfies

4^5=1024=4mod5   satisfies

Nothing bigger will satisfy.

x=0,1,2,3,4   will all satisfy this equation.

c)Which of the residues $0, 1, 2, 3, 4, 5$ satisfy the congruence

\(x^2 + 3x + 2 \equiv 0 \pmod{6}? \)

Give your answer as a list, separated by commas, in order from least to greatest.

\(x^2 + 3x + 2 \equiv 0 \pmod{6}?\\ ​​If \;x=0\\ 0 + 0 + 2 \equiv 2 \pmod{6}?\qquad \mbox{Does not satisfy}\\ ​​If \;x=1\\ 1 + 3+ 2 \equiv 0 \pmod{6}?\qquad \mbox{DOES satisfy}\\ ​​If \;x=2\\ 4 + 6 + 2=12 \equiv 0 \pmod{6}?\qquad \mbox{DOES satisfy}\\ ​​If \;x=3\\ 9 + 9 + 2=20 \equiv 2 \pmod{6}?\qquad \mbox{Does not satisfy}\\ ​​If \;x=4\\ 16 + 12 + 2=30 \equiv 0 \pmod{6}?\qquad \mbox{DOES satisfy}\\ ​​If \;x=5\\ 25 + 15 + 2=42 \equiv 0 \pmod{6}?\qquad \mbox{DOES satisfy}\\\)

So x=1,2,4,5  satisfy the equality.

You should check this.  If you need more explanation then ask for it :)

Thanks Chris

How many ways can richard and hang sit together.

Put a lasso around them. It could be Richard then Hang or hang then Richard but now there are 7 entities. That is 7! ×2 ways.

Now how many ways can (Hang and Richard) and (Thomas and lily) sit together.

Now there are 6 entities so that is 6!×2×2=4×6!

So the number of ways that Richard and hang Do sit together. AND Thomas and Lily DO NOT sit together is

2×7! - 4×6! = 7200

Just like Chris already determined :)

It is still infinity ;)

I'm  assuming this is supposed to be :

135+3x=T

 25+5x=T

Since each equation equals T, we can just set them equal.....and we have

135 + 3x   = 25 + 5x    subtract 3x, 25 from both sides

110  = 2x     divide both sides by 2

55 = x

Actually.....since were solving an equation, we need to take both roots....so  ...

t = ± 11    is correct

Here's the answer....although someone else can probably present it in a more straightforward way........!!!!

Seat Thomas (T) in chair 1  and Lily (L) in any chair from 3 - 7....she has 5 choices

Richard/Hang (RH) can be considered as one entity and can be arranged in 2 ways each

And the other 4 people can be arranged in 4! =  24 ways.....so we have

T 2 L 4 5 6 7 8 ... RH (4 choices  x 2 arrangements each )  x  24  = 192 x 5 choices for Lily = 960 

 If  Thomas is seated in chair 1 and Lily in chair 8 , we have

T 2 3 4 5 6 7 L ...RH (5 choices x 2 arrangements) x 24  = 240

So....when Thomas is seated in chair 1 there are

960 + 240    = 1200  arrangements possible

Next ....seat Thomas in chair 2  and Lily in any of the chairs 4 - 7....she has 4 choices

Following the above notations, we have

1 T 3 4 5 L 7 8    ...RH (3 choices  x 2 arrangements) x  24  = 144 x 4 choices for Lily  = 576

And when Thomas is seated in chair 2 and Lily in chair 8 we have

1 T 3 4 5 6 7 L  ...  RH 4 choices x 2 arrangements X 24 = 192

So....when Thomas is seated in chair 2 there are

576 + 192  = 768  arrangements possible

When Thomas is seated in chair 3, we have the following :

L 2 T 4 5 6 7 8 ...  RH  (4 choices  x  2 arrangements)  x 24   = 192

1 2 T 4 [Lily can occupy any chair 5 - 7]  8   ...  RH (3 choices x 2 arrangements) x 24 x 3 choices for  Lily = 144 x 3 

1 2 T 4 5 6 7 L ....   RH (4 x 2) x 24 =  192

So when Thomas is seated in the third chair we have

192*2 + 144*3  = 816  arrangements possible

And this number of arrangements wll be true when Thomas occupies any of the chairs 3 - 6

So....we have 816 (4) = 3264 possible arrangements when Thomas occupies chairs 3 - 6

When Thomas occupies chair 7, there will be the same number of arrangements as when he occupies chair 2  = 768

And when he occupies chair 8, there will be the same number of arrangements as when he occupies the first chair  = 1200

So we have

1200(2) + 768(2) + 816(4)  = 7200 total arrangements

121 = t² take the square root of both sides

t=sqrt(121)=11

The answer to that is 70

thank  you!!

I assume you want to express

7 x 7 x 5 x 5 x 5 x 5   with exponents  ???....if so....

Write   7 ..   and we have two of them  = 7²

Write 5 ....  and we have  four of them  = 5⁴  

So....the answer  [ without final evaluation] is :

7² * 5⁴    

In general   .....  "a"  multiplied "b"  times    ...... is just .....  a^b

If C'x = -.05 + .001x.......then  the variable cost part of the function becomes :

-.05x + .0005x^2

And the fixed cost part of the function is just  5000

So.....the function is :

C(x)  = -.05x + .0005x^2 + 5000

Proof :

Note that the cost to produce 500 lbs is

C(500)  = $5100

And the cost to produce 5000 lbs is

C(5000) = $17250

So....the extra cost to increase production from 500 to 5000 lbs = $[17250 - 5100] = $12150

sqrt 72   - sqrt8  + sqrt 128

sqrt ( 36*2)  - sqrt (4*2) + sqrt (64*2)

6 sqrt 2   - 2 sqrt 2 + 8 sqrt2

12 sqrt 2

Pi is an infinite number that never ends. 3.14........

pi is infinite but here are the first numbers:

3.1415926535897932

\(\frac{7.5}{2}=x*3.14^2\)

1) First you square 3.14 3.14^2 = 9.8596 

which gives you

\(\frac{7.5}{2}=x*9.8596\)

2) divide 7.5 by 2

7.5/2 = 3.75

and then you get 3.75 = x * 9.8596

3) finally you divide 3.75 by 9.8596 to solve for x

3.75/9.8596 = 0.3803399732240659

and rounded to the nearest tenth is 0.38

4) your final anwser is 0.38=x

For these types of questions I like to asign numbers to each variables and test it out. this is what I did.

a=2 b=3

so I test the first equasion 

\(\frac{2*2*3}{3-2}=\frac{12}{1}=12\)

and now the second 

\(-\frac{2*2*3}{2-3}=-\frac{12}{-1}=12\)

both anwsers match so it is equal