Respuesta :
The icicle starts dripping at 1 x = 1 and stops dripping at x = -7.
Option D is our correct answer.
Given,
An icicle drips at a rate that can be represented by the function:
f(x) = −x2 + 8x − 7, where 0 ≤ x ≤ 10 and x is the number of hours after the sun has risen.
When f(x) is a negative number, the icicle is not dripping.
So when f(x) is positive, the icicle starts dripping.
We need to find the f(x) at -1, 1, 7, and -7.
We have,
f(x) = −x2 + 8x − 7
Putting x = 1
We get,
f(1) = -(1)^2 + 8x1 - 7
= -1 + 8 - 7
= -8 + 8 = 0
It is positive so, the icicle starts dripping.
Putting x = -1
We get,
f(-1) = - (-1)^2 + 8x-1 - 7
= -1 -8 - 7
= -16
It is negative so, the icicle stops dripping.
Putting x = 7
We get,
f(7) = - (7)^2 + 8x7 - 7
= -49 + 56 - 7
= -56 + 56
= 0
It is positive so, the icicle starts dripping.
Putting x = -7
We get,
f(-7) = - (-7)^2 + 8x(-7) - 7
= -49 - 56 - 7
= -112
It is negative so, the icicle stops dripping.
We have,
At x = 1 and 7, the icicle is dripping.
At x = -1 and -7 the icicle is not dripping.
Thus the icicle starts dripping at 1 x = 1 and stops dripping at x = -7.
Option D is our correct answer.
Learn more about the values of a given function that determine conditions here:
https://brainly.com/question/16516764
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