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kumpel [21]
3 years ago
8

Joe barrowed $2,000 from the bank at a rate of 7% simple interest per year. How much will be in your account in 5 years?

Mathematics
1 answer:
timofeeve [1]3 years ago
4 0
For the answer to the question above,
The simple interest formula is I = P * r * t

P is the principal (2,000)
r is the interest rate (7% or 0.07)
t is the time (5)

2000 * 0.07 * 5 = 700

$700.00 is the interest

Joe has to pay $700.00 in interest.
I hope this helps
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A rectangular package sent by a postal service can have a maximum combined length and girth (perimeter of a cross sectio) of 108
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Answer:

The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.

Step-by-step explanation:

This is a optimization with restrictions problem.

The restriction is that the perimeter of the square cross section plus the length is equal to 108 inches (as we will maximize the volume, we wil use the maximum of length and cross section perimeter).

This restriction can be expressed as:

4x+L=108

being x: the side of the square of the cross section and L: length of the package.

The volume, that we want to maximize, is:

V=x^2L

If we express L in function of x using the restriction equation, we get:

4x+L=108\\\\L=108-4x

We replace L in the volume formula and we get

V=x^2L=x^2*(108-4x)=-4x^3+108x^2

To maximize the volume we derive and equal to 0

\dfrac{dV}{dx}=-4*3x^2+108*2x=0\\\\\\-12x^2+216x=0\\\\-12x+216=0\\\\12x=216\\\\x=216/12=18

We can replace x to calculate L:

L=108-4x=108-4*18=108-72=36

The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.

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