19. Bella is putting down patches of sod

To determine the perimeter, we sum the lengths of all sides.

Looking at the diagram, we find the perimeter is calculated as follows:
P = 11 + (x - 2) + (11 - 3) + [(x - 2) - (x - 11)] + (x - 11)
= 11 + x - 2 + 8 + 9 + x - 11
= 2x + 15.

Final expression: 2x + 15

The answer is 1/5; I hope this information is useful.                                                                

The question is:

Examine a differential equation expressed as

y′ = f(αt + βy + γ),

where α, β, and γ are constants. Employ the variable change

z = αt + βy + γ to reformulate the differential equation as a separable equation of the type z′ = g(z).

Answer:

The equation

y′ = f(αt + βy + γ)

can be rephrased as

dy/dt = f(αt + βy + γ).

Our goal is to rewrite this differential equation in the form

z' = g(z), that is dz/dt = g(z).

First, be aware that

dz/dt = (dz/dy) * (dy/dt)...................(1)

Utilizing the substitution

z = αt + βy + γ

as specified,

dz/dy = β..........................................(2)

dy/dt = f(αt + βy + γ) = f(z)............(3)

From equations (2) and (3),

dz/dt = β.f(z) = g(z)

Thus,

z' = g(z)

Where g(z) = βf(z).

Oooooooonnnnnneeeeeeeemmmmmmmmiiiiilllllllliiiiieeee

a(t) = 210 - 5t

(1) What does t represent?

Since t is given in minutes, it stands for time.

Interpreting t as the balloon’s altitude is incorrect since a(t) represents altitude.

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Time elapsed since the balloon starts descending

This is the correct interpretation.

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Time for the balloon to reach ground level is incorrect because that would be a fixed moment, not a variable t.

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(2) What does a(t) represent?

The balloon’s altitude

This is the correct answer.

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Time since descent began is incorrect because that is represented by t.

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Time to reach the ground is inaccurate since a(t) is altitude, not time.

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(3) What does a(5.5) signify?

It does not represent the time to reach 5.5 feet altitude.

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The altitude of the balloon after 5.5 minutes

This is the correct interpretation since a(5.5) is altitude when t = 5.5 minutes.

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It is not the time needed to reach the ground.

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5.5 minutes alone is not correct because a(t) denotes altitude, not time.

a(5.5) refers to altitude at t = 5.5 minutes.