Question

The peak of the tent is at 30 feet and is at a horizontal distance of 20 feet from the left edge. The height of the tent varies at a rate of 1.5 feet with the horizontal distance from the left edge. The equation that models the height of the tent, h, in feet, with respect to the horizontal distance in feet from the left edge, d, is h =___ |d − ___ | + ___ The height of the tent is 22.5 feet at a horizontal distance of ____ feet from its left edge.

a) h = -1.5|d - 20| + 30; d = 30 feet
b) h = 1.5|d - 20| + 30; d = 22.5 feet
c) h = 1.5|d - 20| + 30; d = 20 feet
d) h = -1.5|d - 20| + 30; d = 22.5 feet

Answer 1

The equation that models the tent height in relation to the distance from the left edge is h = -1.5|d - 20| + 30. The height is 22.5 feet at a horizontal distance of 25 feet from the left edge.

Step-by-step explanation:

The problem involves finding an equation that models the height of the tent, h, in feet with respect to the horizontal distance in feet from the left edge, d. At the peak of the tent, the height is 30 feet at a horizontal distance of 20 feet. The height decreases at a rate of 1.5 feet for each additional foot away from this peak, making the slope negative. Therefore, the correct equation should demonstrate a decrease in height as distance increases from the peak, and the height should be reflective of the absolute value of the distance from the 20-foot mark. The equation is h = -1.5|d - 20| + 30.

To find the horizontal distance at which the height of the tent is 22.5 feet, we can substitute h with 22.5 and solve for d. With a little bit of algebra, we can see that when subtracting 30 on both sides and then dividing by -1.5, the absolute value of d - 20 equals 5.

This means that d is either 15 or 25 feet from the left edge. Since we only consider the horizontal distance increasing from the left edge, the correct distance is 25 feet.

Thus, the correct answer is: a) h = -1.5|d - 20| + 30; d = 25 feet.