$\bf \textit{surface area of a sphere}\\\\ SA=4\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} SA=25\pi \end{cases}\implies 25\pi =4\pi r^2 \\\\\\ \cfrac{25\pi }{4\pi }=r^2\implies \cfrac{25}{4}=r^2\implies \sqrt{\cfrac{25}{4}}=r\implies \cfrac{\sqrt{25}}{\sqrt{4}}=r\implies \cfrac{5}{2}=r \\\\[-0.35em] ~\dotfill$

$\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad \qquad \implies V=\cfrac{4\pi \left( \frac{5}{2} \right)^3}{3}\implies V=\cfrac{4\pi \cdot \frac{125}{8}}{3}\implies V=\cfrac{\frac{500\pi }{8}}{~~\frac{3}{1}~~} \\\\\\ V=\cfrac{500\pi }{8}\cdot \cfrac{1}{3}\implies V=\cfrac{500\pi }{24}\implies V=\cfrac{125\pi }{6}\implies V\approx 65.45$

7 0

3 years ago

How many solutions does the equation 5x+17=4(3x−1) have?

Stella [2.4K]

Answer:

one solution = 3

Step-by-step explanation:

Let's solve your equation step-by-step.

5x+17=4(3x−1)

Step 1: Simplify both sides of the equation.

5x+17=4(3x−1)

5x+17=(4)(3x)+(4)(−1)(Distribute)

5x+17=12x+−4

5x+17=12x−4

Step 2: Subtract 12x from both sides.

5x+17−12x=12x−4−12x

−7x+17=−4

Step 3: Subtract 17 from both sides.

−7x+17−17=−4−17

−7x=−21

Step 4: Divide both sides by -7

-7x/-7 = -21/-7 = 3

4 0

3 years ago

If f(x)=X-3/x and g(x) = 5x – 4, what is the domain of (fog)(x)? NEED HELP FAST!!

dedylja [7]

Answer:

Step-by-step explanation:

This is function composition. We will take the g function and plug it into the f function wherever we see an x. That will look like this when it's done but before it's simplified:

$f(g(x))=\frac{5x-4-3}{5x-4}$ and that can be simplified down to

$f(g(x))=\frac{5x-7}{5x-4}$

The domain of this function will be all real numbers EXCEPT for the one(s) that cause the denominator to become undefined. Set the denominator equal to 0 and solve for x:

5x - 4 = 0 so

5x = 4 and

x = 4/5

In other words, D = {x | x ≠ 4/5}

6 0

3 years ago