the length of a rectangle is three times it’s width. if the area of the rectangle is 300 yd^2, find its perimeter.

Mathematics

1 answer:

Mashutka [201]3 years ago

6 0

Answer:

80 yards

Step-by-step explanation:

Using the area formula, A = lw, set up an equation where w represents the width.

The length can be represented by 3w because it is 3 times the width:

A = lw

300 = (3w)(w)

300 = 3w²

Solve for w:

300 = 3w²

100 = w²

10 = w

So, the width is 10 yards.

The length will be 30 yards since the length is 3 times the width.

Then, add the lengths and widths together to find the perimeter:

10 + 10 + 30 + 30

= 80

So, the perimeter is 80 yards

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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

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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