Question

Please help, its formula manipulation, only respond if u know how to get the answer, thank you​

Answer 1

Answer:

Problem 1:

$r=\frac{3V}{2 \pi h^2}$

Problem 2:

$h=\frac{3V}{b^2}$

Problem 3:

The radius is $\frac{25}{\pi}$ cm.

Problem 4:

The width is 15 cm.

Step-by-step explanation:

Problem 1:

We want to solve $V=\frac{2\pi rh^2}{3}$ for $r$.

$V=\frac{2\pi rh^2}{3}$

Multiply both sides by 3:

$3V=2\pi r h^2$

Rearrange the multiplication using commutative property:

$3V=2\pi h^2 \cdot r$

We want to get $r$ by itself so divide both sides by what $r$ is being multiplied by which is $2\pi h^2$.

$\frac{3V}{2 \pi h^2}=r$

$r=\frac{3V}{2 \pi h^2}$

Problem 2:

We want to solve for $h$ in $V=\frac{b^2h}{3}$.

Multiply both sides by 3:

$3V=b^2h$

We want $h$ by itself so divide both sides by what $h$ is being multiply by; that is divide both sides by $b^2$.

$\frac{3V}{b^2}=h$

$h=\frac{3V}{b^2}$

Problem 3:

The circumference formula for a circle is $2\pi r$. We are asked to solve for the radius when the circumference is $50$ cm.

$2\pi r=50$

Divide both sides by what r is being multiply by; that is divide both sides by $2\pi$:

$r=\frac{50}{2\pi}$

Reduce fraction:

$r=\frac{25}{\pi}$

The radius is $\frac{25}{\pi}$ cm.

Problem 4:  

The perimeter of a rectangle is $2w+2L$ where $w$ is the width and $L$ is the length.

We are asked to find w, the width, for when L, the length, is 5, and the perimeter is 40.

So we have this equation to solve for w:

$40=2w+2(5)$

Simplify the 2(5) part:

$40=2w+10$

Subtract both sides by 10:

$30=2w$

Divide both sides by 2:

$\frac{30}{2}=w$

Simplify the fraction:

$15=w$

The width is 15 cm.