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BaLLatris [955]

3 years ago

12

A shipping company uses an inclined conveyor belt to load or unload packages. The dock is 15 feet above ground. The base of the

conveyor belt is 40 feet from the dock. What is the length the conveyor belt?

1 answer:

alexgriva [62]3 years ago

7 0

Hey there! :D

Think of this like a triangle. The dock is 15 feet above ground. It is the side of the triangle. The line connecting the bottom of the dock to the base of the conveyor belt is 40 feet. This is like the base.

The conveyor belt itself is at a diagonal, and should be the hypotenuse.

Use the Pythagorean theorem.

a^2+b^2=c^2

15^2+40^2= c^2

225+1,600= c^2

Add the values together.

1,825= c^2

Find the square root of 1,825.

c= 42.7 (rounded to the nearest tenth)

The conveyor belt is 42.7 feet long.

I hope this helps!
~kaikers

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Answer:

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Step-by-step explanation:

Given

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First, calculate the car's slope (m)

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From the table, we have:

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$m = -\frac{1}{40}$

Calculate the equation using:

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$y = -\frac{1}{40}x + 1.5+13.5$

$y = -\frac{1}{40}x + 15$

$m = -\frac{1}{40}$ implies that for every mile traveled, the car uses 1/40 gallon of gas

Also:

$y = -\frac{1}{5}x + 31$ --- The van

By comparison to: $y = mx + b$

$m = -\frac{1}{5}$

This implies that for every mile traveled, the van uses 1/5 gallon of gas.

By comparison:

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This means that the car uses less gas

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We have:

$y = -\frac{1}{5}x + 31$ --- The van

$y = -\frac{1}{40}x + 15$ --- The car

Equate both

$-\frac{1}{5}x + 31 =-\frac{1}{40}x + 15$

Collect like terms

$\frac{1}{40}x -\frac{1}{5}x =-31 + 15$

$\frac{1}{40}x -\frac{1}{5}x =-16$

Take LCM

$\frac{x - 8x}{40} = -16$

$\frac{- 7x}{40} = -16$

Solve for -7x

$-7x = -640$

Solve for x

$x = \frac{640}{7}$

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