Answer:
35 miles per gallon.
Step-by-step explanation:
We need to simplify 175/5 into 35/1 to make it into a unit rate. So, 35 miles per gallon is the answer.
C can be found using pythagoras theorem. c2=a2+b2. Now, b is not given, but we know that cos(theta)=b/c=>b=c*cos(theta). Substituting b in the above relation, c2=a2+c2(cos(theta))^2=>c2=a2/(1-cos((theta))^2). c is the squareroot of c2. Hence c=sqrt(2/(1-cos((theta))^2))
Base case: For
, the left side is 2 and the right is
, so the base case holds.
Induction hypothesis: Assume the statement is true for
, that is

We want to show that this implies truth for
, that

The first
terms on the left reduce according to the assumption above, and we can simplify the
-th term a bit:


so the statement is true for all
.