A rectangular parking lot has a perimeter of 800 ft. An inequality representing the parking lot is x(400 − x) > 30,000.

Question

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Answer 1

x(400-x) > 30000

400x - x² - 30000 > 0

x² - 400x + 30000 < 0

(x - 300)(x - 100) < 0

For a product to be negative, one of these terms must be negative, and the other positive.

The inequality becomes an equality when x = 300 and x = 100

To find out when the inequality is true consider the regions (-inf, 100), (100, 300), (300, inf)

On (-inf, 100), both x - 300 and x - 100 are negative, so the product is positive.

On (100, 300), x - 300 < 0 and x - 100 > 0, so the product is negative.

On (300, inf), x - 300 > 0 and x - 100 > 0, so the product is positive.

Thus, the product is negative only on (100, 300)

This is the solution.