Answer:
135
Step-by-step explanation:
m^2 = 3
Cube m^2
(m^2)^3 = 3^3
m^(2*3) = 27
m^6 = 27
Now multiply by 5
5 * m^6 = 5*27
5 m^6 =135
I think you have to first separate the integral:1/(1+v^2) + v/(1+v^2),
so the integral of the first term is ArcTan (v) and for the integral of the second term i recommend you to do a change of variable:
y= 1+v^2
so
dy= 2v
and
v= dy/2and then you substitute:v/(1+v^2) = (1/2)(dy/y)
and the integral is
(1/2) (In y)finally you plug in the initial variables:
(1/2)(In [1+v^2])
so the total integral is:
ArcTan (y) + (1/2)(In [1+v^2])
Answer:
Step-by-step explanation:
If we roll a multiple of 5 we will get one of the following:
5, 10, 15 , 20.
None of these is a perfect square so they are mutually exlusive,
Answer:
Part a) 
Part b) 
Part c) 
Step-by-step explanation:
Part a) What is the volume of your friend's swimming pool?
we know that
The volume of a rectangular prism is equal to

substitute the values

Part b) Your swimming pool is in the shape of a cylinder with a diameter of 16 feet and has the same volume as your friend's pool. What is the height of your pool?
we know that
The volume of a cylinder is equal to

we have

----> the radius is half the diameter
substitute and solve for h



Part c) While you were on vacation, 6 inches of water evaporated from your pool. About how many gallons of water evaporated from your pool?
remember that

so

Find the volume of water for 

so
the volume of water evaporated is equal to

convert to gallons
remember that

so
