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Find all 3 sides of the red triangle.

AC = BC = 5    |   ∠ACB = 90º    |    ∠PCQ = 45º    |    ∠ACP = ∠BCQ = 22.5º

Let M be a midpoint of AB

AB = sqrt (AC² + BC²)

PQ = 2 * [tan(PCM) * CM]              ( CM = AM = BM )

AP = BQ = 1/2 (AB - PQ)

1.    angle ADC = angle ADB                                              AD is perpendicular to BC (given) so both are 90^o

2.    side AD = side AD                                                       equals itself  

3.    angle CAD = angle BAD                                              AD bisects angle CAB (given) so each half is equal 

4.    therefore triangle ADC congruent to triangle ADB       angle-side-angle theorem   

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Good Work.  I'm sure everyone here is glad to hear it and proud of you.  

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it costs 23.50 to enter an amusement park and $0.25 to ride a ride. you have $24 write an equation that represents the number of r rides you can ride    

                  24.00 – 23.50                 0.50    

N_rides  =   ————————      =   ———  =   2 rides    

                        0.25                          0.25   

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r= 2     haha

13 is 10% of 130

The probability = [(5  nCr  4 * 5^1) + (5  nCr  5 * 5^0) * 6] / 6^5 = 13 / 648

n****r x n****r = c**n

The product of my numbers is 15.

m + b = 13.

Sorry about that!

I meant to say AP^2 + BQ^2 = PQ^2

Find the product of all x such that the expression (x^2 - 4)/(x^2 - 1) is undefined.   

                                 x² – 4   

The expression is   ————   

                                 x² – 1   

When a denominator equals zero, the expression is undefined. 

So, in this case, it is undefined at  x = +1  

By the way, the denominator would factor to (x + 1)(x – 1)

Factoring would be helpful in a more complicated expression,  

but this one is simple enough it wasn't necessary. 

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sixty two point nine zero two five six.      is one way

Which angle is the right-angle, A B or C ?

thank you! :)

thank you! good luck on your test too!

thank you so much!

Thanks anonymous!

The first graph has the x values within the range 0 to 2pi.

Oh oops, I see. Do you know how I could get the graph within the range of [0, 2pi]? Thanks!

The volume of a cylinder is 60 cubic centimeters. The radius of the cylinder is 2. What is the number of cubic centimeters in the volume of the sphere that circumscribes the cylinder?

Hello Guest!

\(\color{blue}V_{zyl}=\pi r^2h\\ h=\frac{V_{zyl}}{\pi r^2}=\frac{60\ cm^3}{\pi \cdot 2^2\ cm^2}\)

\(h=\frac{15\ cm}{\pi}\)

\(R^2=(\frac{h}{2})^2+r^2=\frac{225\ cm^2}{\pi ^2}+2^2\ cm^2\\ R^2 =26.797\ cm^2\\ \color{blue} R=5.1766\ cm\)

\(V_{sphere}=\frac{4}{3}\pi \cdot R^3=\frac{4}{3}\pi \cdot 5.1766^3\ cm^3\)

\(V_{sphere}=581.065\ cm^3\)

  !

one inch each