Answer:
[tex]t = 1.45[/tex] or [tex]t = 0.86[/tex]
Step-by-step explanation:
Given
[tex]h=3+37t-16t^2[/tex]
Required
Find all values of t when height is 23 feet
To solve this, we simply substitute 23 for h
[tex]23=3+37t-16t^2[/tex]
Collect like terms
[tex]16t^2 - 37t - 3 + 23=0[/tex]
[tex]16t^2 - 37t +20=0[/tex]
Solve t using quadratic formula;
[tex]t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
Where a = 16, b =-37 and c = 20
[tex]t = \frac{-(-37)\±\sqrt{(-37)^2 - 4*16*20}}{2*16}[/tex]
[tex]t = \frac{37\±\sqrt{(-37)^2 - 4*16*20}}{2*16}[/tex]
[tex]t = \frac{37\±\sqrt{1369 - 1280}}{32}[/tex]
[tex]t = \frac{37\±\sqrt{89}}{32}[/tex]
[tex]t = \frac{37\±9.43}{32}[/tex]
[tex]t = \frac{37+9.43}{32}[/tex] or [tex]t = \frac{37-9.43}{32}[/tex]
[tex]t = \frac{46.43}{32}[/tex] or [tex]t = \frac{27.57}{32}[/tex]
[tex]t = \frac{46.43}{32}[/tex] or [tex]t = \frac{27.57}{32}[/tex]
[tex]t = 1.45[/tex] or [tex]t = 0.86[/tex]
