To get the *percent increase* from week 1 to week 2, we calculate the change in distance from week 1 to week 2 (13.5 - 12.5 = 1 mile) over the week 1 distance (12.5 miles). Doing that, we find that Matthew increased his distance by
1/12.5 = 0.08, or 8%
We’re given that he’ll increase his distance by the same percentage from week 2 to 3, so to find his week 3 distance, we can find 8% of the week 2 distance and add that on. 8% of 13.5 miles is 0.08 x 13.5 = 1.08 miles, so by week 3, he’ll be running 13.5 + 1.08 = 14.58 miles.
Answer:
c
Step-by-step explanation:
Here's how this works:
Get everything together into one fraction by finding the LCD and doing the math. The LCD is sin(x) cos(x). Multiplying that in to each term looks like this:
![[sin(x)cos(x)]\frac{sin(x)}{cos(x)}+[sin(x)cos(x)]\frac{cos(x)}{sin(x)} =?](https://tex.z-dn.net/?f=%5Bsin%28x%29cos%28x%29%5D%5Cfrac%7Bsin%28x%29%7D%7Bcos%28x%29%7D%2B%5Bsin%28x%29cos%28x%29%5D%5Cfrac%7Bcos%28x%29%7D%7Bsin%28x%29%7D%20%3D%3F)
In the first term, the cos(x)'s cancel out, and in the second term the sin(x)'s cancel out, leaving:

Put everything over the common denominator now:

Since
, we will make that substitution:

We could separate that fraction into 2:
×
and 
Therefore, the simplification is
sec(x)csc(x)