Need help with this function problem

Mathematics

1 answer:

kotykmax [81]2 years ago

4 0

Answer:

see attached

Step-by-step explanation:

To find the inverse function, solve ...

x = f(y)

x = (y^7)/7 -4 . . . . . . . use the definition of f(x)

x +4 = (y^7)/7 . . . . . . add 4

7(x +4) = y^7 . . . . . . multiply by 7

(7(x +4))^(1/7) = y . . take the 7th root

The inverse function is the one shown in the attachment.

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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)=−4.9t2+121t

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