Question

For each of the following questions, solve for the unknown quantity by rearranging the given equation.For numerical answers, make sure to express all answers in scientific notation with the proper number ofsignificant figures. Be careful to write out all units and convert if necessary.a. F=GMm/r^2a. M =b. r =b. M=kxa^3/p^2a. P =b. a =

Answer 1

a. F=GMm/r^2; a. M =

`M = (Fr^(2) )/(Gm)`

a. F=GMm/r^2; b. r =

`r = \sqrt{(GMm)/(F) \\}`

b. M=kxa^3/p^2; a. P =

`p = \sqrt{(kxa^(3))/(M)}`

b. M=kxa^3/p^2; b. a =

`a = \sqrt[3]{(Mp^(2))/(kx) }`

Explanation:

For a. F=GMm/r^2; a. M =

To solve for M, we will rearrange the given equation F=GMm/r^2 such that M is the subject of the formula

From

F=GMm/r^2

`F = (GMm)/(r^(2) )`

First, Cross multiplication, we then get

`Fr^(2) = GMm`

Now, divide both sides by
`Gm`

`(Fr^(2) )/(Gm) = (GMm)/(Gm) \\`

The equation becomes

`(Fr^(2) )/(Gm) = M`

∴
`M = (Fr^(2) )/(Gm)`

For a. F=GMm/r^2; b. r =

Also, to solve for r, we will rearrange the given equation F=GMm/r^2 such that r is the subject of the formula

From

F=GMm/r^2

`F = (GMm)/(r^(2) )`

First, Cross multiplication, we then get

`Fr^(2) = GMm`

Now, divide both sides by
`F`, Such that we have

`(Fr^(2) )/(F) = (GMm)/(F) \\`

Then,
`r^(2) = (GMm)/(F) \\`

∴
`r = \sqrt{(GMm)/(F) \\}`

For b. M=kxa^3/p^2; a. P =

To solve for P, we will rearrange the given equation M=kxa^3/p^2 such that P becomes the subject of the formula

From

M=kxa^3/p^2

`M = (kxa^(3))/(p^(2) ) \\`

First, Cross multiply, we then get

`Mp^(2) = kxa^(3)`

Divide both sides by
`M`, such that the equation becomes

`(Mp^(2) )/(M) = (kxa^(3))/(M)`

Then,
`p^(2) = (kxa^(3))/(M)`

∴
`p = \sqrt{(kxa^(3))/(M)}`

For b. M=kxa^3/p^2; b. a =

To solve for a, we will rearrange the given equation M=kxa^3/p^2 such that a becomes the subject of the formula

From

M=kxa^3/p^2

`M = (kxa^(3))/(p^(2) ) \\`

First, Cross multiply, we then get

`Mp^(2) = kxa^(3)`

Now, Divide both sides by
`kx`, such that the equation gives

`(Mp^(2))/(kx) = ( kxa^(3))/(kx)`

Then,
`(Mp^(2))/(kx) = a^(3)`

`a^(3) = (Mp^(2))/(kx)`

∴
`a = \sqrt[3]{(Mp^(2))/(kx) }`