PLEASE HELP (must show work) Show all work to factor x4 - 17x2 + 16 completely.

Mathematics

1 answer:

Firdavs [7]3 years ago

4 0

There i hope this helped

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insens350 [35]

4 is your answer

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Alenkasestr [34]

NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by

$h(t)=-4.9t^2+121t+283$

The sea level is represented by h = 0, therefore, to find the corresponding time when h splashes into the ocean we have to solve for t the following equation:

$h(t)=0\implies-4.9t^2+121t+283=0$

Using the quadratic formula, the solution for our problem is

$\begin{gathered} t=\frac{-(121)\pm\sqrt{(121)^2-4(-4.9)(283)}}{2(-4.9)} \\ =\frac{121\pm142.083778...}{9.8} \\ =\frac{121+142.083778...}{9.8} \\ =26.8452834694... \end{gathered}$

The rocket splashes after 26.845 seconds.

The maximum of this function happens at the root of the derivative. Differentiating our function, we have