Use the Pythagorean theorem for this. (a^2+b^2=c^2)
a=9, b=12, c=x
9^2+12^2=c^2
81 + 144 = c^2
225 = c^2
c =15
the answer is c
6a. By the convolution theorem,
6b. Similarly,
7. Take the Laplace transform of both sides, noting that the integral is the convolution of 
and 
.
where 
. Then 
, and
We have the partial fraction decomposition,
Then we can easily compute the inverse transform to solve for f(t) :
Answer:
27 ounces of blueberry juice. 40 ounces of soy milk. 13 ounces of banana flavoring.
Step by Step:
4 + 1.3 = 5.3, This is how much of the smoothie is made up of the soy milk and banana flavoring, 5.3 ounces.
So to find the amount of blueberry juice in the smoothie you have to subtract 8-5.3. This finds the remaining part of the smoothie, which is the blueberry juice. 8-5.3 = 2.7
2.7 ounces of blueberry juice in each smoothie.
Now you have to multiply every ingredient by 10, since there are 10 smoothies.
4 * 10 = 40
1.3 * 10 = 13
2.7 * 10 = 27
You need 40 ounces of soymilk, 13 ounces of banana flavoring, and 27 ounces of blueberry juice to make 10, 8-ounce smoothies.
