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A model rocket is launched with an initial upward velocity of 140 fts. The rocket's height h (in feet) after t seconds is given by the following.h=140t -16t^2Find all values of t for which the rocket's height is 68 feet.Round your answer(s) to the nearest hundredth(If there is more than one answer, use the "or" button.)



Answer :

Answer:

8.23secs and 0.53secs

Explanation:

Given the expression for calculating the height reached by a rocket as;

[tex]h=140t-16t^2[/tex]

If the rocket's height is 68feet, then;

[tex]\begin{gathered} 68=140t-16t^2 \\ 16t^2-140t+68=0 \\ 4t^2-35t+17=0 \end{gathered}[/tex]

Factorize;

[tex]\begin{gathered} t=\frac{-(-35)\pm\sqrt[]{(-35)^2-4(4)(17)}}{2(4)} \\ t=\frac{35\pm\sqrt[]{1225-272}}{8} \\ t=\frac{35\pm\sqrt[]{953}}{8} \\ t=\frac{35\pm30.8}{8} \\ t=\frac{35+30.8}{8}or\frac{35-30.8}{8} \\ t=\frac{65.8}{8}or\frac{4.2}{8} \\ t=8.23or0.53 \end{gathered}[/tex]

Hence the required values of t are 8.23secs and 0.53secs

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