Question

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

Answer 1

Problem 1:

`r=(3V)/(2 \pi h^2)`

Problem 2:

`h=(3V)/(b^2)`

Problem 3:

The radius is
`(25)/(\pi)` cm.

Problem 4:

The width is 15 cm.

Explanation:

Problem 1:

We want to solve
`V=(2\pi rh^2)/(3)` for
`r`.

`V=(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`.

`(3V)/(2 \pi h^2)=r`

`r=(3V)/(2 \pi h^2)`

Problem 2:

We want to solve for
`h` in
`V=(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`.

`(3V)/(b^2)=h`

`h=(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=(50)/(2\pi)`

Reduce fraction:

`r=(25)/(\pi)`

The radius is
`(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:

`(30)/(2)=w`

Simplify the fraction:

`15=w`

The width is 15 cm.