Length times width times height gives you the volume of things
If Eric earns $56 or more means
t is greater or equal to 56
If you multiply out the first side of the equation, (x + 5)³, it's equal to the second side.
x³ + 5³ = x³ + 5³, so any value of x would work.
x = "any real number" would be your answer, unless you can't type. then I think anything would work (I'm not certain though!) :)
Answer:
![-2.0213\times 10^{-7}GMm\text{ J}](https://tex.z-dn.net/?f=-2.0213%5Ctimes%2010%5E%7B-7%7DGMm%5Ctext%7B%20J%7D)
Step-by-step explanation:
Since, the force of gravity is,
![F = -\frac{GMm}{r^2}](https://tex.z-dn.net/?f=F%20%3D%20-%5Cfrac%7BGMm%7D%7Br%5E2%7D)
Where,
G = gravitational constant,
M = mass of earth,
m = mass of the particle,
r = distance of particle from centre of the earth,
∵ 7500 km =
meters
9400 km =
meters
Thus, work done by the force of gravity,
![W=\int_{7.5\times 10^6}^{9.4\times 10^6}F. dr](https://tex.z-dn.net/?f=W%3D%5Cint_%7B7.5%5Ctimes%2010%5E6%7D%5E%7B9.4%5Ctimes%2010%5E6%7DF.%20dr)
![=-\int_{7.5\times 10^6}^{9.4\times 10^6}\frac{GMm}{r^2}dr](https://tex.z-dn.net/?f=%3D-%5Cint_%7B7.5%5Ctimes%2010%5E6%7D%5E%7B9.4%5Ctimes%2010%5E6%7D%5Cfrac%7BGMm%7D%7Br%5E2%7Ddr)
![=GMm[\frac{1}{r}]_{7.5\times 10^6}^{9.4\times 10^6}](https://tex.z-dn.net/?f=%3DGMm%5B%5Cfrac%7B1%7D%7Br%7D%5D_%7B7.5%5Ctimes%2010%5E6%7D%5E%7B9.4%5Ctimes%2010%5E6%7D)
![=GMm(\frac{1}{9.4\times 10^6}-\frac{1}{7.5\times 10^6})](https://tex.z-dn.net/?f=%3DGMm%28%5Cfrac%7B1%7D%7B9.4%5Ctimes%2010%5E6%7D-%5Cfrac%7B1%7D%7B7.5%5Ctimes%2010%5E6%7D%29)
![=GMm(\frac{7.5-9.4}{9.4\times 10^6})](https://tex.z-dn.net/?f=%3DGMm%28%5Cfrac%7B7.5-9.4%7D%7B9.4%5Ctimes%2010%5E6%7D%29)
![=-GMm(\frac{1.9}{9.4\times 10^6})](https://tex.z-dn.net/?f=%3D-GMm%28%5Cfrac%7B1.9%7D%7B9.4%5Ctimes%2010%5E6%7D%29)
![\approx -2.0213\times 10^{-7}GMm\text{ J}](https://tex.z-dn.net/?f=%5Capprox%20-2.0213%5Ctimes%2010%5E%7B-7%7DGMm%5Ctext%7B%20J%7D)
Where,
![G = 6.67408\times 10^{-11} \text{ }m^3 kg^{-1} s^{-2}](https://tex.z-dn.net/?f=G%20%3D%206.67408%5Ctimes%2010%5E%7B-11%7D%20%5Ctext%7B%20%7Dm%5E3%20kg%5E%7B-1%7D%20s%5E%7B-2%7D)
![M=5.972\times 10^24 \text{ kg}](https://tex.z-dn.net/?f=M%3D5.972%5Ctimes%2010%5E24%20%5Ctext%7B%20kg%7D)