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 of
significant figures. Be careful to write out all units and convert if necessary.
3.
F=GMm/r^2

a. M =
b. r =
M=kxa^3/p^2

a. P =
b. a =

For F=GMm/r^2

a.

b.

M=kxa^3/p^2

a.

b.

Step-by-step explanation:

To solve for the unknown quantity, we will make the unknown quantity the subject of the given equation.

For F=GMm/r^2

a. M =

F=GMm/r^2

The first thing to do is cross multiply, so that the equation gives

Now, divide both sides of the equation by , we then get

Then,

Hence,

b. r =

F=GMm/r^2

Likewise, we will first cross multiply, we then get

Now, divide both sides by , so that the equation becomes

∴

Then,

For M=kxa^3/p^2

a. P =

M=kxa^3/p^2

The first thing to do is cross multiply, so that the equation becomes

Now, divide both sides by M, we then get

∴

Then,

b. a =

M=kxa^3/p^2

Also, we will first cross multiply to get

Then, divide both sides of the equation by to get

∴

Then,

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)