4

Set 14: Quadratic Equations (Advanced)

Explanation

Answer: A

A gutter is made by turning up the edges of a 12-inch wide sheet of metal. What depth maximizes the cross-sectional area?

A.

3 inches

✓ Correct
B.

4 inches

C.

6 inches

D.

2 inches

Detailed Explanation

Choice A is correct. Choice A is the correct answer. 1. Setup: Let xx be the depth (height of turned-up sides). The base width is 12−2x12- 2 x. 2. Area Function: A(x)=x(12−2x)=−2x2+12xA(x) = x(12 - 2 x) = -2 x^2 + 12 x. 3. Maximize: Vertex x=−12/(2(−2))=3x = -12 / (2(-2)) = 3. 4. Result: Depth is 3 inches. Choice B is incorrect. Choice C is incorrect because width would be 0. Choice D is incorrect.

Key Steps:

•

The correct answer is 3 inches

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.
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