I don't see a square root sign anywhere, so I'll assume the integral is

First complete the square:

Now in the integral, substitute

so that

Under this change of variables, we have

so that

Under the right conditions, namely that cos(<em>t</em>) > 0, we can further reduce the integrand to


Expand the sine term as

Then


So the integral is

Answer:
14.04 miles per hour
Step-by-step explanation:
The problem is asking for Izumi's speed. The formula of speed is:
- s =
, where "s" means speed, "d" means distance and "t" means time.
The problem is also asking for the unit<u> miles per hou</u>r (
) so, this means that we have to know how many miles Izumi ran, given that the problem only mentioned<u> yards (110 yards).</u>
Let's convert 110 yards to miles, provided that he Izumi ran 1,760 yards in a mile.
- 110 yards ÷ 1760
= 0.0625 miles (this is the distance covered by Izumi in miles)
Let's go back again to the formula: s = 
s =
= 0.0039 
Since, the we arrived at a miles per second unit, we have to convert it to miles per hour.
So, if a minute has 60 seconds, then an hour has 3,600 seconds.
Thus, 0.0039
× 3,600
= 14.04 miles per hour (the answer)
Answer:
1256
Step-by-step explanation:
Given the function F(x)=1256(1.24)^x, the initial value occurs at x = 0
Substitute x = 0 into the function;
F(0)=1256(1.24)^0
f(0) = 1256(1) (any value raise to sero is 1)
f(0) = 1256
hence the initial value is 1256