Mel slides down waterslide A, and Victor slides down waterslide B. After 2 seconds, Mel was 50 feet in the air, and after 5 seconds, she was 35 feet in the air. After 1 second, Victor was 60 feet in the air, and after 4 seconds, he was 50 feet in the air. Who was descending at a faster rate?

Mel: (2, 50) and (5, 35)

Victor: (1, 60) and (4, 50)

Mel’s rate of change is__.That means that her height in the air decreases _ feet every second.

Victor’s rate of change is _ . That means that his height in the air decreases ___ feet every second.

The first thing you should do for this case is to find both slopes by applying the following equation:
m = ((y2) - (y1)) / ((x2) - (x1))
Mel: (2, 50) and (5, 35)
m1 = ((35) - (50)) / ((5) - (2))
m1 = -5 feet / s
Victor: (1, 60) and (4, 50)
m2 = ((50) - (60)) / ((4) - (1))
m2 = -3.333333333 feet / s

answer:
Mel was descending at a faster rate
Mel's rate of change is negative. That means that your height in the air decreases 5 feet every second.
Victor's rate of change is negative. That means that his height in the air decreases 3.33 feet every second.

nishantwork777 nishantwork777 · Answer 2 · 2021-11-01T07:29:07+01:00

The height of Mel in the air is decreasing at a faster rate than victor's height in the air.

Mel's rate of change is -5 feet per second. That means that her height in the air decreases 5 feet every second.

Victor's rate of change is -3.33 feet per second. That means that his height in air decreases 3.33 feet every second.

Given information:

Mel slides down water-slide A and Victor slides down water-slide B.

After 1 second, height achieved by [tex]\rm{Mel}= 50\; \text{Ft}[/tex]

After 5 seconds, the height remained is 35 feet.

In another case,

The height achieved by Victor after 1 second is 60 feet.

The height remained after 4 second is 50 feet.

Now, the expression is used for evaluating the slope of the equation are formulated below:

[tex]\bold{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Where, [tex]m[/tex] is the slope and [tex]x[/tex] and [tex]y[/tex] are respective coordinates.

Hence, for Mel's case, apply the formula of slope and solve it further:

[tex]\begin{aligned}m_1&=\dfrac{35-50}{5-2} \\m_1&=-5 \end{aligned}[/tex]

So, the rate of change of Mel's height is 5 feet per second.

And for victor's case, slope will be:

[tex]m_2=\dfrac{50-60}{4-1} \\\\m_2=-3.33[/tex]

The rate of change of victor's height is 3.33 feet per second.

Mel's rate of change is -5 feet per second. That means that her height in the air decreases 5 feet every second.

Victor's rate of change is -3.33 feet per second. That means that his height in air decreases 3.33 feet every second.

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