To find the height 4 seconds after launch, plug in t = 4 in the formula for h: h(4) = -16(4^{2}) + 128(4) = -256 + 512 = 256 ft. The domain of h is the set of all t values for which h(t) is defined. Since h(t) must be nonnegative, to find the domain we must solve the inequality -16t^{2 }+ 128t ≥ 0, i.e., -16t(t - 8) ≥ 0. The zeros of -16t(t - 8) are t = 0 and t = 8. We verify the truth of the inequality in the intervals t < 0, 0 < t < 8, and t > 8, using the sign test. For t < 0 we may take t = -1 as a test point: -16(-1)(-1 - 8) = 16(-9) < 0. So the inequality is false for t < 0. For 0 < t < 8, we may take t = 1 as a test point: -16(1)(1 - 8) = -16(-7) > 0. Thus, the inequality is true for 0 < t < 8. Finally, for t > 8, we may take t = 10 as a test point: -16(10)(10 - 8) = -16(10)(2) < 0. Therefore, the inequality is false for t > 8. Since t = 0 and t = 8 also satisfy the inequality, we determine that the solution set is [0, 8]. So the domain of h is the closed interval [0, 8].

Eugene E.

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 wrong09/05/19

Eugene E.

09/05/19

Milan H.

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

Eugene E.

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?09/05/19

Eugene E.

09/06/19

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? Thanks09/05/19