Question

1. The length of a rectangle is 13 more than the width, w. If the area of the rectangle is 30 square inches (in"), what are the dimensions of the rectangle?

2. The height of a flare fired from the deck of a ship in distress can be modeled by h =- 16€ + 104t + 56, where h is the height of the flare above the water and t is the time in seconds. When does the flare hit the water? (Hint: Start by pulling out gef and making ×? positive)

Answer 1

1) The dimensions of the rectangle are:

width = 24.2 in

length = 37.2 in

2) The time at which the flare hits the water is: 7 seconds

How to solve Quadratic equations?

1) We are given:

Length of rectangle = W + 13

Area = 30 in²

Thus:

W (W + 13) = 30

W² + 13W = 900

W² + 13W - 900 = 0

Using quadratic formula, we have:

W = {-13 ± √[13² - 4(1)(-900)]} / 2(1)

w = {-13 ± √(169 + 3600)} / 2

w = {-13 ± √(3769)} / 2

This gives:

w = 24.2 in

Thus:

length = 24.2 + 13 = 37.2 in

2) The equation is given as:

h = -16t² + 104t + 56

where:

h is the height of the flare above the water.

t is the time in seconds

The flare hit the water when h = 0

Thus:

-16t² + 104t + 56 = 0

Divide the equation by 8 to get:

-2t² + 13t + 7 = 0

Factorize to get:

(-2t - 1)(t - 7) = 0

We will take the positive one and so:

t = 7 secs