**Answer:**

Take a look at the 'proof' below

**Step-by-step explanation:**

The questions asks us to determine the anti-derivative of the function f(x) = 4x^3 sec^2 x^4. Let's start by converting this function into integral form. That would be the following:

Now all we have to do is solve the integral. Let's substitute 'u = x^4' into the equation 'du/dx = 4x^3.' We will receive dx = 1/4x^3 du. If we simplify a bit further:

Our hint tells us that d/dx tan(x) = sec^2(x). Similarly in this case our integral boils down to tan(u). If we undo the substitution, we will receive the expression tan(x^4). Therefore you are right, the first option is an anti-derivative of the function f(x) = 4x^3 sec^2 x^4.

**Answer:**

C. No e = h + 2

**Step-by-step explanation:**

The answer is (No. e = h + 2) because first of all 4 times 2/3 is 6 but 8 multiplied by 2/3 is not 10, So, A is wrong.

B is also wrong because it is basically the same thing as A.

D is not right because 6 - 2 is not 8.

So, the answer is C. No e = h + 2.

Hope this helps! :)

**Answer:**

A, the ratio stays the same for every pair.

**Step-by-step explanation:**

**Answer:**

C. 0.85 cups

**Step-by-step explanation:**

4.25/5 = 0.85