Start with

We observe that both fractions are not defined if
. So, we will assume
.
We multiply both numerator and denominator of the first fraction by 3 and we sum the two fractions:

We multiply both sides by
:

We move everything to one side and solve the quadratic equation:

We check the solution:

which is true
It depends on what you mean by the delimiting carats "^"...
Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for

.
In that case, you want to find the antiderivative,

Complete the square in the denominator:

Now substitute

, so that

. Then

which simplifies to

Now, recall that

. But we want the substitution we made to be reversible, so that

which implies that

. (This is the range of the inverse sine function.)
Under these conditions, we have

, which lets us reduce

. Finally,

and back-substituting to get this in terms of

yields
Answer:

Step-by-step explanation:
1. Calculate the number of cups

2. Calculate the number of bird feeders

Answer:
1. at 1 hour, 3 miles is the distance.
2. at 0 hours, 0 miles is the distance.
3. at 3 hours, 9 miles is the distance.