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little help here?

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I got this problem I can't wrap my head around. help?

H(T) =-4.9t^t + 40t

when hight (H) is 75, what is seconds (T)

Guest May 8, 2017
#1
+7324
+4

I think this is what the equation is:

H(t) = -4.9t^2 + 40t

We want to know what t is when h(t) = 75

So plug in 75 for h(t) and solve for t.

75 = -4.9t^2 + 40t

Subtract 75 from both sides.

0 = -4.9t2 + 40t - 75

Now we can use the quadratic formula to solve for t.

$$t = {-40 \pm \sqrt{40^2-4(-4.9)(-75)} \over 2(-4.9)}\\~\\t={-40 \pm \sqrt{130} \over -9.8}\\~\\ t=\frac{-40+\sqrt{130}}{-9.8}\qquad\text{or}\qquad t=\frac{-40-\sqrt{130}}{-9.8}$$

t ≈ 5.245 seconds      or      t ≈ 2.918 seconds

hectictar  May 9, 2017
#2
+7324
+4

Imagine you threw a baIl up in the air and every second you wrote this information down: (what second it was, the height of the ball at that second). For example....at second 1, the height was 35.1 units...and you would write down: (1, 35.1).

Then you plotted all these points on a graph and drew a red line connecting the points. This is what your line would look like:

And the question is, " After how many seconds was the ball was 75 units up in the air? "

hectictar  May 9, 2017