Respuesta :
Answer:
a. F=GMm/r^2; a. M =
[tex]M = \frac{Fr^{2} }{Gm}[/tex]
a. F=GMm/r^2; b. r =
[tex]r = \sqrt{\frac{GMm}{F} \\}[/tex]
b. M=kxa^3/p^2; a. P =
[tex]p = \sqrt{\frac{kxa^{3}}{M}}[/tex]
b. M=kxa^3/p^2; b. a =
[tex]a = \sqrt[3]{\frac{Mp^{2}}{kx} }[/tex]
Step-by-step 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
[tex]F = \frac{GMm}{r^{2} }[/tex]
First, Cross multiplication, we then get
[tex]Fr^{2} = GMm[/tex]
Now, divide both sides by [tex]Gm[/tex]
[tex]\frac{Fr^{2} }{Gm} = \frac{GMm}{Gm} \\[/tex]
The equation becomes
[tex]\frac{Fr^{2} }{Gm} = M[/tex]
∴ [tex]M = \frac{Fr^{2} }{Gm}[/tex]
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
[tex]F = \frac{GMm}{r^{2} }[/tex]
First, Cross multiplication, we then get
[tex]Fr^{2} = GMm[/tex]
Now, divide both sides by [tex]F[/tex], Such that we have
[tex]\frac{Fr^{2} }{F} = \frac{GMm}{F} \\[/tex]
Then, [tex]r^{2} = \frac{GMm}{F} \\[/tex]
∴ [tex]r = \sqrt{\frac{GMm}{F} \\}[/tex]
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
[tex]M = \frac{kxa^{3}}{p^{2} } \\[/tex]
First, Cross multiply, we then get
[tex]Mp^{2} = kxa^{3}[/tex]
Divide both sides by [tex]M[/tex], such that the equation becomes
[tex]\frac{Mp^{2} }{M} = \frac{kxa^{3}}{M}[/tex]
Then, [tex]p^{2} = \frac{kxa^{3}}{M}[/tex]
∴ [tex]p = \sqrt{\frac{kxa^{3}}{M}}[/tex]
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
[tex]M = \frac{kxa^{3}}{p^{2} } \\[/tex]
First, Cross multiply, we then get
[tex]Mp^{2} = kxa^{3}[/tex]
Now, Divide both sides by [tex]kx[/tex], such that the equation gives
[tex]\frac{Mp^{2}}{kx} = \frac{ kxa^{3}}{kx}[/tex]
Then, [tex]\frac{Mp^{2}}{kx} = a^{3}[/tex]
[tex]a^{3} = \frac{Mp^{2}}{kx}[/tex]
∴ [tex]a = \sqrt[3]{\frac{Mp^{2}}{kx} }[/tex]
