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iragen [17]
3 years ago
13

A cat chases a mouse. The cat is originally 4 feet behind the mouse, which is running in the same direction along the same route

as the cat. If the cat's speed is 17 feet per second and the mouse's speed is 12 feet per second, how long will it take the cat to catch up with the mouse? (how many seconds?)
Mathematics
1 answer:
Verdich [7]3 years ago
8 0

Step-by-step explanation:

The position of the mouse at time t is 4 + 12t.

The position of the cat at time t is 17t.

When the positions are equal:

4 + 12t = 17t

4 = 5t

t = 0.8

It takes 0.8 seconds.

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Answer:

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Step-by-step explanation:

Given

y=c_1e^{-x}cosx+c_2e^{-x}sinx

Required

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Rewrite the expression as:

y=c_1e^{\alpha x}cos(\beta x)+c_2e^{\alpha x}sin(\beta x)

Where

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For a homogeneous linear differential equation, the repeated value m is given as:

m = \alpha \± \beta i

Substitute values for \alpha and \beta

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In complex numbers:

i^2 = -1

So, the expression becomes:

m^2 + 2m + 1 = -1

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m^2 + 2m + 1 +1= -1+1

m^2 + 2m + 2= 0

This corresponds to the homogeneous linear differential equation

y" + 2y' + 2y = 0

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