Answer:
Using either method, we obtain: 
Step-by-step explanation:
a) By evaluating the integral:
![\frac{d}{dt} \int\limits^t_0 {\sqrt[8]{u^3} } \, du](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%20%5Cint%5Climits%5Et_0%20%7B%5Csqrt%5B8%5D%7Bu%5E3%7D%20%7D%20%5C%2C%20du)
The integral itself can be evaluated by writing the root and exponent of the variable u as: ![\sqrt[8]{u^3} =u^{\frac{3}{8}](https://tex.z-dn.net/?f=%5Csqrt%5B8%5D%7Bu%5E3%7D%20%3Du%5E%7B%5Cfrac%7B3%7D%7B8%7D)
Then, an antiderivative of this is: 
which evaluated between the limits of integration gives:
and now the derivative of this expression with respect to "t" is:
b) by differentiating the integral directly: We use Part 1 of the Fundamental Theorem of Calculus which states:
"If f is continuous on [a,b] then
is continuous on [a,b], differentiable on (a,b) and 
Since this this function 
is continuous starting at zero, and differentiable on values larger than zero, then we can apply the theorem. That means:
Answer:
(1/7, 1)
Step-by-step explanation:
By "answer," you probably meant "solution." What is the "solution of the system of linear equations
- 5y = - 5
+ 7x +6y=7
The first eqation can be solved for y: y = 1. Substitute 1 for y in the secon equation. Then 7x + 6(1) = 7, or 7x = 1, or x = 1/7.
The solution to this system is (1/7, 1)
B) If we subtract females who prefer dogs from the total that prefer dogs we will know how many males prefer dogs.
290-180=110
So 110 males prefer dogs.
c) 180 females prefer dogs and 12 prefer fish, so 180+12=192 females do not prefer cats.
DBE is similar to ABC by the SAS Similarity Theorem
