Answer: A
<u>Explanation:</u>
NOTES:
d = 650 meters
t = 10 seconds
**********************************
v = d/t
= 650 meters/10 seconds
= 65 meters/second
Answer:
R_cm = 4.66 10⁶ m
Explanation:
The important concept of mass center defined by
R_cm = 1 / M ∑ x_i m_i
where M is the total mass, x_i and m_i are the position and masses of each body
Let's apply this expression to our case.
Let's set a reference frame where the axis points from the center of the Earth to the Moon,
R_cm = 1 / M (m_earth 0 + m_moon d)
the total mass is
M = m_earth + m_moon
the distance from the Earth is zero because all mass can be considered to be at its gravimetric center
let's calculate
M = 5.98 10²⁴ + 7.35 10²²
M = 6.0535 10₂⁴24 kg
we substitute
R_cm = 1 / 6.0535 10²⁴ (0 + 7.35 10²² 3.84 )
R_cm = 4.66 10⁶ m
We don't know how many of ANY color are in the bag right now, so there's no way to calculate an answer.
What Tom has to do is make sure that the number of marbles that are NOT blue is NINE TIMES the number of blue ones in the bag.
Answer:
The rate of change of the area when the bottom of the ladder (denoted by
) is at 36 ft. from the wall is the following:
![\frac{dA}{dt}|_{b=36}=-571.2\, ft^2/s](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%7C_%7Bb%3D36%7D%3D-571.2%5C%2C%20ft%5E2%2Fs)
Explanation:
The Area of the triangle is given by
where
(by using the Pythagoras' Theorem) and
is the length of the base of the triangle or the distance between the bottom of the ladder and the wall.
The area is then
![A=\sqrt{l^2-b^2}b](https://tex.z-dn.net/?f=A%3D%5Csqrt%7Bl%5E2-b%5E2%7Db)
The rate of change of the area is given by its time derivative
![\frac{dA}{dt}=\frac{d}{dt}\left(\sqrt{l^2-b^2}\cdot b\right)](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%3D%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%28%5Csqrt%7Bl%5E2-b%5E2%7D%5Ccdot%20b%5Cright%29)
![\implies \frac{dA}{dt}=\frac{d}{dt}\left(\sqrt{l^2-b^2}\right)\cdot b+\frac{db}{dt}\cdot\sqrt{l^2-b^2}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cfrac%7BdA%7D%7Bdt%7D%3D%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%28%5Csqrt%7Bl%5E2-b%5E2%7D%5Cright%29%5Ccdot%20b%2B%5Cfrac%7Bdb%7D%7Bdt%7D%5Ccdot%5Csqrt%7Bl%5E2-b%5E2%7D)
Product rule
Chain rule
![\implies\frac{dA}{dt}=-\frac{1}{\sqrt{l^2-b^2}}\cdot b^2\cdot \frac{db}{dt}+\sqrt{l^2-b^2}}\cdot \frac{db}{dt}](https://tex.z-dn.net/?f=%5Cimplies%5Cfrac%7BdA%7D%7Bdt%7D%3D-%5Cfrac%7B1%7D%7B%5Csqrt%7Bl%5E2-b%5E2%7D%7D%5Ccdot%20b%5E2%5Ccdot%20%5Cfrac%7Bdb%7D%7Bdt%7D%2B%5Csqrt%7Bl%5E2-b%5E2%7D%7D%5Ccdot%20%5Cfrac%7Bdb%7D%7Bdt%7D)
![\implies\frac{dA}{dt}=\frac{db}{dt}\left(-\frac{1}{\sqrt{l^2-b^2}}\cdot b^2+\sqrt{l^2-b^2}}\right)](https://tex.z-dn.net/?f=%5Cimplies%5Cfrac%7BdA%7D%7Bdt%7D%3D%5Cfrac%7Bdb%7D%7Bdt%7D%5Cleft%28-%5Cfrac%7B1%7D%7B%5Csqrt%7Bl%5E2-b%5E2%7D%7D%5Ccdot%20b%5E2%2B%5Csqrt%7Bl%5E2-b%5E2%7D%7D%5Cright%29)
In here we can identify
,
and
.
The result is then
![\frac{dA}{dt}=8\left(-\frac{1}{\sqrt{39^2-36^2}}\cdot 36^2+\sqrt{39^2-36^2}}\right)=-571.2\, ft^2/s](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%3D8%5Cleft%28-%5Cfrac%7B1%7D%7B%5Csqrt%7B39%5E2-36%5E2%7D%7D%5Ccdot%2036%5E2%2B%5Csqrt%7B39%5E2-36%5E2%7D%7D%5Cright%29%3D-571.2%5C%2C%20ft%5E2%2Fs)