What is the average rate of change of an object between falling 4 feet and falling 64 feet? *Please explain

Mathematics

1 answer:

Daniel [21]2 years ago

6 0

Average rate of change can be calculated by the following

Δy/Δx

Our Δx refers to displacement.
Δx = 4 - 64 = -60

Our Δy refers to our Δf(x)

To get our f(x) values, we must plug in 64 and 4 into the function f(x)
f(64) = 8√64 = 64
f(4) = 8√4 = 16
Δf(x) = 16 - 64 = -48

So our rate of change is -60/-48 = 0.8

I believe the answer should be positive 0.8, but that's my best estimate.

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telo118 [61]

Answer: the x-intercept is (-10,0), the y-intercept is (0,45/2)

Explanation:

First, we need to determine the function describing the line.

From the table, it is obvious that the y values increase by 9 every increase of 4 of the x values. So, the slope is 9/4 and the function looks like this:

$y = m x+ b = \frac{9}{4}x + b$

with the y-intercept (or bias) b still unknown. This can be determined by using one of the point from the table, like so:

$-18 = \frac{9}{4}\cdot 2+b\\\implies b = -18 -\frac{9}{2}=\frac{45}{2}\\y = \frac{9}{4}x+\frac{45}{2}$

The above function form makes it easy to read off the y-intercept, which is (0,45/2) or (0,22.5). The x-intercept is obtained by setting y = 0 and solving for x:

$y = \frac{9}{4}x+\frac{45}{2}\\0 = \frac{9}{4}x+\frac{45}{2}\\-\frac{45}{2}=\frac{9}{4}x\\x = -10$