Step-by-step explanation:
The first step is wrong. It claims that
but it is not true. It is attempting to simplify the fraction by cancelling the x^3 terms from 9x^3 and 2x^3.
However, to perform this operation, all terms in the fraction must be divided by x^3. But this will mean
Question:
A lighthouse is located on an island 3 miles from the closest point on a straight shoreline. If the lighthouse light rotates clockwise at a constant rate of 9 revolutions per minute, how fast does the beam of light move towards the point on the shore closest to the island when it is 52 miles from that point
Answer:
The beam of light moves at miles/min
Step-by-step explanation:
This question is illustrated with the attached image
Taking the instructions in the question, one at a time.
A revolution of 9 per minute implies that:
Take tan of the angle in the attachment:
Differentiate both sides with respect to time
Rewrite as:
In calculus:
-- Chain rule
So:
In trigonometry:
So:
Recall that:
Recall that:
Multiply both sides by 3
miles/min
Hence:
The beam of light moves at miles/min
