Milan H.

# precalc question: find the domain of this function?

A firecracker is launched straight up, and its height is a function of time, h(t) = −16t2 + 128t, where h is the height in feet and t is the time in seconds, with t = 0 corresponding to the instant it launches. What is the height 4 seconds after launch? What is the domain of this function?

By:

Milan H.

I am doing this problem on a site called WileyPlus, and I enter the answer as (-infinity, infinity) to solve for the domain (as required by the site), and it says the answer is incorrect. Could you please help? Thanks
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09/05/19

Eugene E.

tutor
Actually, being a physical problem, h(t) has to be nonnegative, so to find the domain, we would have to solve the inequality -16t^2 + 128t >= 0, or -16t(t - 8) >= 0. This yields solution 0 <= t <= 8. So the domain is [0, 8]. Sorry for the confusion.
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09/05/19

Milan H.

what would the answer be for the problem -11t^2 +88t? I got 0<=t<=-8 but the site said that was also wrong
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09/05/19

Eugene E.

tutor
You have it wrong because you put -8 for the right endpoint.
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09/05/19

Milan H.

so then should it be -8>=t>=0?
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09/05/19

Eugene E.

tutor
No, there are two issues: (1) you have it written such that -8 > 0 even though -8 is negative, and (2) -8 is not one of the endpoints. It should be 8. So the domain should be the same as the one above, [0, 8].
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09/05/19

Milan H.

so for the problem -11t^2 +88t, the solution would be what exactly? with the greater of less than or equal to signs?
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09/05/19

Eugene E.

tutor
0 <= t <= 8
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09/06/19

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