HELPPPPP!! Last attempt
2 answers:
You might be interested in
Answer:
The visitor should run approximately 14.96 mile to minimize the time it takes to reach the island
Step-by-step explanation:
From the question, we have;
The distance of the island from the shoreline = 1 mile
The distance the person is staying from the point on the shoreline = 15 mile
The rate at which the visitor runs = 6 mph
The rate at which the visitor swims = 2.5 mph
Let 'x' represent the distance the person runs, we have;
The distance to swim =
The total time, 't', is given as follows;
The minimum value of 't' is found by differentiating with an online tool, as follows;
At the maximum/minimum point, we have;
Simplifying, with a graphing calculator, we get;
-4.72·x² + 142·x - 1,070 = 0
From which we also get x ≈ 15.04 and x ≈ 0.64956
x ≈ 15.04 mile
Therefore, given that 15.04 mi is 0.04 mi after the point, the distance he should run = 15 mi - 0.04 mi ≈ 14.96 mi
Therefore, the distance to run, x ≈ 14.96 mile
Take into account, that in general, a cosine function of amplitude A, period T and vertical translation b, can be written as follow:
In the given case, you have:
A = 4
T = 3π/4
b = -3
By replacing you obtain:
Hence, the answer is:
f(x) = 4cos(8/3 x) - 3