Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

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. Determine the values when the icicle starts and stops dripping.

Sagot :

LammettHash

Find when f(x) = 0. By factorizing, we have

-x² + 8x - 7 = - (x - 7) (x - 1) = 0

so either x - 7 = 0 or x - 1 = 0, or simply x = 1 or x = 7.

Split the domain into three intervals, and check the sign of f(x) over each interval at some test point in the interval. The sign will tell you when the icicle is dripping (positive) or not (negative).

• [0, 1) : at x = 0, we have f(0) = -7 < 0

• (1, 7) : at x = 2, we have f(2) = 5 > 0

• (7, 10] : at x = 8, we have f(8) = -7 < 0

This tells us that the icicle is not dripping when 0 ≤ x < 1, begins to drip when x = 1, drips for the duration of 1 < x < 7, stops dripping when x = 7, and keeps on not dripping when 7 < x ≤ 10.

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.