It must be a and c, as these are the only two with four closed sides
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.
Bernardo travels the same distance at 25mph as he does at 50mph. However, since 25mph is only half of 50 mph, he must travel twice as long at 25mph. If you call the time he traveled 50mph "t", then
<span>t+2t=3 </span>
<span>3t=3 </span>
<span>t=1 </span>
<span>This means he traveled 1 hour at 50mph. In this time, he traveled 50 miles. He traveled the same distance at 25mph, so his total distance was </span>
<span>50miles+50miles=100miles </span>
<span>so the round trip was 100 miles.</span>