Answer:
P(A)=0.5
P(B)=0.5
Step-by-step explanation:
It's known that P(A and B) = P(A) * P(B) "When A and B are independent.
Now, suppose that P(A) = P(B)
then
P(A) * P(B) = P(A) * P(A) = (P(A))^2
finally
(P(A))^2 = 0.25
![P(A) = \sqrt{0.25}](https://tex.z-dn.net/?f=P%28A%29%20%3D%20%5Csqrt%7B0.25%7D)
The answer to this question is:
<span>An ant looks up to the top of a tree with an angle of elevation of 38. if the ant is 43 feet from the base of the tree, what is the height of the tree, to the nearest tenth?
"33.6 Ft"
Hoped this helped, Vickicoward7545
Your Welcome :)</span>
a. Salt flows into tank A at a rate of
(<em>y</em>(<em>t</em>)/500 lb/gal) * (50 gal/min) = <em>y</em>(<em>t</em>)/10 lb/gal
and out at a rate of
(<em>x</em>(<em>t</em>)/500 lb/gal) * (50 gal/min) = <em>x</em>(<em>t</em>)/10 lb/gal
so the net rate of change of the amount of salt in tank A is
![x'(t)=\dfrac{y(t)}{10}-\dfrac{x(t)}{10}](https://tex.z-dn.net/?f=x%27%28t%29%3D%5Cdfrac%7By%28t%29%7D%7B10%7D-%5Cdfrac%7Bx%28t%29%7D%7B10%7D)
Similarly, you would find
![y'(t)=\dfrac{x(t)}{10}-\dfrac{y(t)}{10}](https://tex.z-dn.net/?f=y%27%28t%29%3D%5Cdfrac%7Bx%28t%29%7D%7B10%7D-%5Cdfrac%7By%28t%29%7D%7B10%7D)
b. We have
![x'=-\dfrac x{10}+\dfrac y{10}\implies x''=-\dfrac{x'}{10}+\dfrac{y'}{10}](https://tex.z-dn.net/?f=x%27%3D-%5Cdfrac%20x%7B10%7D%2B%5Cdfrac%20y%7B10%7D%5Cimplies%20x%27%27%3D-%5Cdfrac%7Bx%27%7D%7B10%7D%2B%5Cdfrac%7By%27%7D%7B10%7D)
Notice that <em>x'</em> = -<em>y'</em>, so
![x''=-{2x'}{10}\implies 5x''+x'=0](https://tex.z-dn.net/?f=x%27%27%3D-%7B2x%27%7D%7B10%7D%5Cimplies%205x%27%27%2Bx%27%3D0)
Solve for <em>x</em>: the characteristic equation
![5r^2+r=r(5r+1)=0](https://tex.z-dn.net/?f=5r%5E2%2Br%3Dr%285r%2B1%29%3D0)
has roots
and
, so
![x(t)=C_1+C_2e^{-t/5}](https://tex.z-dn.net/?f=x%28t%29%3DC_1%2BC_2e%5E%7B-t%2F5%7D)
Again using the fact that <em>y'</em> = -<em>x'</em>, we then find
![x'(t)=-\dfrac{C_2}5e^{-t/5}\implies y'(t)=\dfrac{C_2}5e^{-t/5}\implies y(t)=C_1-C_2e^{-t/5}](https://tex.z-dn.net/?f=x%27%28t%29%3D-%5Cdfrac%7BC_2%7D5e%5E%7B-t%2F5%7D%5Cimplies%20y%27%28t%29%3D%5Cdfrac%7BC_2%7D5e%5E%7B-t%2F5%7D%5Cimplies%20y%28t%29%3DC_1-C_2e%5E%7B-t%2F5%7D)
Given that <em>x</em>(0) = 0 and <em>y</em>(0) = 10, we find
![\begin{cases}0=C_1+C_2\\10=C_1-C_2\end{cases}\implies C_1=5,C_2=-5](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D0%3DC_1%2BC_2%5C%5C10%3DC_1-C_2%5Cend%7Bcases%7D%5Cimplies%20C_1%3D5%2CC_2%3D-5)
There are 30 cuboids in that one cube. (6*5) or (10*3)!
Answer:
.6 meters
Step-by-step explanation:
We need to take the total length and divide it by 4, since that is the number of rods we want and they are all the same length
2.4/4 =.6 meters
Each rod will be .6 meters long