Write an equation from the information given: A rectangle is twice as long as it is wide. The perimeter of the rectangle is 18.

Mathematics

1 answer:

Agata [3.3K]4 years ago

3 0

Let width = x, Therefore the length must equal 2x

Therefore insert these values on the sides of a rectangle.

Add: 2x + 2x + x + x = 18

Therefore 6x = 18

x = 3

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TEA [102]

Answer:

Simple springs obey Hooke's Law. Hooke's Law states that the force on a spring is proportional to it's displacement from it's resting length:

F = -k*x

Where F is the force, x is how far the string is stretched or compressed, and k is a proportionality constant called the spring constant. The negative sign is because the spring resists stretching.

In this case, we can solve for k using the first case:

(100N) = -k * (5cm)

k = ???

And plug that answer in to find x in the second case:

(360N) = -k * x

This is a "Hooke's Law" problem: the restoring force required to compress or stretch a spring is proportional to the distance the spring is deformed. You can figure solve it by setting up a proportion equation and then using the algebraic tool of cross multiplication to solve for the unkown "stretch".

1) set up the proportion equation

100 = 360

5 x

2) cross multiply to get a linear equation

100x = 5*360

3) solve for x

100x = 1800

x = 18

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