# The height of the tide measured at a seaside community varies according to the number of hours t after midnight. If the height h, in feet, is currently given by the equation #h=-1/2t^2+6t-9#, when will the tide first be at 6 ft?

At

or, #t = [12 + 2 sqrt 6]/2 , [12 - 2 sqrt 6]/2

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To find when the tide will first be at 6 ft, set the equation h = -1/2t^2 + 6t - 9 equal to 6 and solve for t:

-1/2t^2 + 6t - 9 = 6

-1/2t^2 + 6t - 9 - 6 = 0

-1/2t^2 + 6t - 15 = 0

Now, use the quadratic formula to solve for t:

t = [-b ± √(b^2 - 4ac)] / 2a

Substitute a = -1/2, b = 6, and c = -15 into the formula:

t = [-(6) ± √((6)^2 - 4(-1/2)(-15))] / (2 * (-1/2))

t = [-(6) ± √(36 - 30)] / (-1)

t = [-(6) ± √(6)] / (-1)

t ≈ [-(6) ± √(6)] / (-1)

Therefore, the tide will first be at 6 ft approximately at t ≈ 0.79 hours after midnight and at t ≈ 11.21 hours after midnight.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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