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A rock is dropped from the top of a​ 2000-foot building. After ​second, the rock is traveling feet per second. After ​seconds, the rock is traveling feet per second. Let y be the rate of descent and x be the number of seconds since the rock was dropped. Part A: Write a linear equation that relates time x to rate y. (Hint: Use the ordered pairs (1,32) and (2,64) ) Part B: Use this equation to determine the rate of travel of the rock 17 seconds after it was dropped.

Respuesta :

MrRoyal

Answer:

[tex]y = 32x[/tex]

The rate is 224 ft/s

Step-by-step explanation:

Solving (a):

Given

[tex](x_1,y_1) = (1,32)[/tex]

[tex](x_2,y_2) = (2,64)[/tex]

Required

Determine the linear equation

First, we need to determine the slope using

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

[tex]m = \frac{64 - 32}{2 - 1}[/tex]

[tex]m = \frac{32}{1}[/tex]

[tex]m = 32[/tex]

The equation is then calculated using:

[tex]y - y_1= m(x - x_1)[/tex]

[tex]y - 32= 32(x - 1)[/tex]

[tex]y - 32= 32x - 32[/tex]

Add 32 to both sides

[tex]y - 32 + 32= 32x - 32 + 32[/tex]

[tex]y = 32x[/tex]

Solving (b):

Given

[tex]x = 7[/tex]

Required

Determine y

We have that:

[tex]y = 32x[/tex]

Substitute 7 for x

[tex]y=32 * 7[/tex]

[tex]y=224[/tex]

Hence, the rate is 224 ft/s