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The figure shows two concentric circles. If the length of chord AB is 100 units and chord AB is tangent to the smaller circle, what is the area of the shaded region? Express your answer in terms of pi.

Hello Guest!

\(R^2=50^2+r^2\\ R^2-r^2=50^2\\ R^2-r^2=2500\)

\(A=\pi R^2-\pi r^2\\ A=(R^2-r^2) \pi \\ \color{blue}A=2500 \pi\ square\ units\)

That's what I did and that's where I am confused

Set the 2 equations equal to each other. You will get 

x³+8y³=x+8y.

Try to solve this now.

You have to wait around 24 hours, then restate the issue. In my case, I was reopening another person's 3 month old question. 

I wasn't logged in as Nacirema, sry.

A cube of edge length s > 0 has the property that its surface area is equal to the sum of its volume and two  times its edge length. Compute the sum of all possible values of s.    

                                             Surface area            =    6s²  

                                             Volume                     =     s³  

                                       Twice the edge length    =    2s  

Set up the equality                                   s³ + 2s  =  6s²   

Rearrange terms                             s³ – 6s² + 2s  =  0   

Factor out an s                            s • (s² – 6s + 2)  =  0  

Divide both sides by s                          s² – 6s + 2  =  0  

I couldn't factor that so  

used the binomial formula  

The answers for s I got were           s = 3 + sqrt(7)  and  s = 3 – sqrt(7)  

Adding them together                      Their sum is   6          

_.

Find the equations of the median from vertex A to the opposite side BC using the points below:

A(9, 5), B(2, 5), C(4, 1)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

1/   Equation of the median   y = 1/3x + 2

2/   Length of the median (round your answer to the nearest tenth) = √40 = 6.3

Rhombus ABCD has a perimeter of 148, and one of its diagonals has a length of 20. How long is the other diagonal?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

d = 2{ sqrt [(148/4)²- (20/2)²]}

Angle AOB = 4 * 28 = 112 degrees

∠BAC ≅ ∠BCE = 48º

∠ABC  ≅ ∠ACB  ≅ ∠ACD = 66º

Your answer is very clear.  

If you want help with Latex this is a good site to start on.  What you have written would not be terribly difficult in LaTex but to start,

the fraction 1/2   is just

\frac{1}{2}

\frac means that what follows is to be written as a fraction.   

The numerator goes in the first set of parentheses and the denominator goes in the second set.

Easy peazy.

=\(\frac{1}{2}\)

I need help on this, too.

The smallest such number ==459

 so first we can simplify $4^x$ into $2^2x$. So $2^2x$+$2^x$+$1$=$111$, next is $2^2x$+$2^x$=$110$, add so that it is $2^3x=110, take log on both sides and you get 2.260453

pls check if I am correct and don't submit answer until verify

36 / 25 ==1.44^(1/3)==1.1292432 daily growth rate

Ln(1.1292432)  *  45 days ==5.46965

25  x  e^5.46965 ==25  x  237.377 ==5,934 - Bees at the end of 45 days.

No '=' sign or explaination in those expressions?

36 = 25 e ^{k 3}       soooo  k = .121548

25 e ^{.121548 (45)} =5934 bees at 45 days

48314 ( 1 + .025)³² = ............ people at end of 32 years

1   Molar mass: 64.066 g/mol    for sulfur dioxide

       43.2/64.066 x   6.022 x 10²³   molecules

2   Molar mass: 36.458 g/mol    for HCl

      ( 1.23 x 1024 )  / (6.022 x 10²³ )    *   36.458   = ............ gm HCl

What are you studying right now? I need a little more detail, thanks! :)

That's all my teacher put literally