Is there a way to solve this without l'hopital's rule?
1 answer:
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If you do this with a complex set of fractions and let
K = G Me m_space be the same in both parts, there should be some cancellation.
W_earth = 180 lbs
W_earth = K /3900 miles^2
W_space =K /(3900 + 850)^2
180 / W_space = k/3900^2
x = k / (4750)^2
![\frac{180}{Wspace} = \frac{ \frac{k}{3900^{2} } }{ \frac{k}{4750^{2}} /[tex]\\Now you need to invert and multiply the bottom fraction on the left.\\[tex] \frac{180}{x} {=} \frac{k}{3900^{2}} {*} \frac{4750^{2}}{k}](https://tex.z-dn.net/?f=%20%5Cfrac%7B180%7D%7BWspace%7D%20%3D%20%20%5Cfrac%7B%20%5Cfrac%7Bk%7D%7B3900%5E%7B2%7D%20%7D%20%7D%7B%20%5Cfrac%7Bk%7D%7B4750%5E%7B2%7D%7D%20%2F%5Btex%5D%5C%5CNow%20you%20need%20to%20invert%20and%20multiply%20the%20bottom%20fraction%20on%20the%20left.%5C%5C%5Btex%5D%20%5Cfrac%7B180%7D%7Bx%7D%20%7B%3D%7D%20%5Cfrac%7Bk%7D%7B3900%5E%7B2%7D%7D%20%7B%2A%7D%20%5Cfrac%7B4750%5E%7B2%7D%7D%7Bk%7D%20)
The ks cancel out.
You are left with 180/x = 4750^2 / 3900^2 Now cross multiply
180 * 3900^2 = 4750^2 = x
180 * 3900^2 / 4750^2 = x
180 * 0.67413 = x
x = 121 pounds. Weight is a force, but because all the units on one side are equivalent to the units on the other, the conversions become part of k. Normally you would have to do the conversions, but not in this particular case.
K = G Me m_space be the same in both parts, there should be some cancellation.
W_earth = 180 lbs
W_earth = K /3900 miles^2
W_space =K /(3900 + 850)^2
180 / W_space = k/3900^2
x = k / (4750)^2
The ks cancel out.
You are left with 180/x = 4750^2 / 3900^2 Now cross multiply
180 * 3900^2 = 4750^2 = x
180 * 3900^2 / 4750^2 = x
180 * 0.67413 = x
x = 121 pounds. Weight is a force, but because all the units on one side are equivalent to the units on the other, the conversions become part of k. Normally you would have to do the conversions, but not in this particular case.