Question

Vint is testing ceiling fans in a factory. For one of the tests, he switches the fan on, and after it attains a maximum speed of 500 rotations per minute (rpm), he switches the fan back off, recording the amount of time it takes for the fan to completely stop spinning. The given equation models Vint's test, where x represents time in seconds and y represents the speed in rotations per minute. The equation has been graphed as shown.

Assuming that the test was complete when the fan stopped spinning completely, how long was the test?

A. 100 seconds

B. 10 seconds

C. 20 seconds

D. 500 seconds

Answer 1

C. 20 seconds

Explanation:

We want to know when y=0.

We are finding the x intercepts.

The first y is when it started and the second y=0 is when it stops.

Looking at the graph y=0 at x=0 and y=0 at x=20

The fan started at time 0 and stopped at 20 seconds.

The difference is the length of the test.

20-0 = 20

20 seconds

Answer 2

20 seconds

Explanation:

Given :

`y=-5x^2+100x`

Where x represents time in seconds and y represents the speed in rotations per minute.

To Find : Assuming that the test was complete when the fan stopped spinning completely, how long was the test?

Solution:

Since we are supposed to find how long will it take to stop the fan completely

We assumed that test was complete when the fan stopped spinning completely

i.e. y = Speed = 0

So, Substitute y = 0 in the equation
`y=-5x^2+100x`

⇒
`0=-5x^2+100x`

⇒
`5x^2=100x`

⇒
`5x=100`

⇒
`x=(100)/(5)`

⇒
`x=20`

Thus it took 20 seconds to stop the fan

Hence the test was 20 seconds long.