Consider a slide shaped like a right triangle. The base of the slide is 45 feet away from the ladder. The top of the slide is 20 feet high. a) What is the slope of the slide. b) write an equation for the line that the slide would form. c) Lets say you were standing at the bottom of the slide and walked 27 feet closer to the ladder. How high is the slide at this point? d)If the slide was 50 feet long, what would be the new slope?

Question

Consider a slide shaped like a right triangle. The base of the slide is 45 feet away from the ladder. The top of the slide is 20 feet high. a) What is the slope of the slide. b) write an equation for the line that the slide would form. c) Lets say you were standing at the bottom of the slide and walked 27 feet closer to the ladder. How high is the slide at this point? d)If the slide was 50 feet long, what would be the new slope?

Answer 1

This guy is wrong^^

Answer 2

slope is rise/run = 20/45

y = 20/45 x

at 27 feet in, the height would be 20/45 * 27 = 12 ft

If the slide were 50 ft long, then its base would be √(50^2-20^2) = √2100 = 45.8 ft away.

New slope is 20/45.8

Hmmph. Not much difference, eh? The original slide was 49.2 feet long. Poor choice of changes.

Answer 3

a) To find the slope of the slide, we need to use the formula: slope = rise / run. The rise is the vertical distance and the run is the horizontal distance.

In this case, the rise of the slide is 20 feet (the height) and the run is 45 feet (the base length).

So, the slope of the slide is: slope = 20 / 45 = 4/9.

b) To write an equation for the line that the slide forms, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.

The slope in this case is 4/9, and to find the y-intercept, we need to determine the point where the line intersects the y-axis. Since the top of the slide is 20 feet high, the point (0,20) is on the line.

Using this information, the equation for the line that the slide forms is: y = (4/9)x + 20.

c) If you were standing at the bottom of the slide and walked 27 feet closer to the ladder, you would be at a horizontal distance of 45 - 27 = 18 feet.

To find out how high the slide is at this point, we can substitute this x-value into the equation of the line:

y = (4/9)(18) + 20
y = 8 + 20
y = 28 feet.

So, the slide would be 28 feet high at this point.

d) If the slide was 50 feet long, we need to find the new slope. The run of the slide is now 50 feet.

Using the formula for slope, we can calculate the new slope:

slope = rise / run
slope = 20 / 50
slope = 2/5.

So, the new slope of the slide would be 2/5.