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3 years ago

13

Calculate the scale factor. A. k=1/7 B. k=5/7 C. k=7/5 D. k=5

1 answer:

Shtirlitz [24]3 years ago

6 0

Answer is Option B = 5/7

Explanation:

A scale factor is a number which scales, or multiplies, some quantity. In the equation y = Kx, K is the scale factor for x. K is also the coefficient of x, and may be called the constant of proportionality of y to x.

For big pictures or maps, images should be drawn without affecting the shape in a small paper. Hence dimension of x is reduced to y with constant proporiton k which is scale factor

Here we find that original length of PC = 21

In image P'C = 15

Hence scale factor=15/21 = 5/7

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A cylinder shaped can needs to be constructed to hold 400 cubic centimeters of soup. The material for the sides of the can costs

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The dimensions of the can that will minimize the cost are a Radius of 3.17cm and a Height of 12.67cm.

Step-by-step explanation:

Volume of the Cylinder=400 cm³

Volume of a Cylinder=πr²h

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Total Surface Area of a Cylinder=2πr²+2πrh

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Cost of the materials for the sides=0.03 cents per square centimeter

Cost of the Cylinder=0.06(2πr²)+0.03(2πrh)

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Therefore:

$C(r)=0.12\pi r^2+0.06 \pi r(\frac{400}{\pi r^2})$

$C(r)=0.12\pi r^2+\frac{24}{r}$

$C(r)=\frac{0.12\pi r^3+24}{r}$

The minimum cost occurs when the derivative of the Cost =0.

$C^{'}(r)=\frac{6\pi r^3-600}{25r^2}$

$6\pi r^3-600=0$

$6\pi r^3=600$

$\pi r^3=100$

$r^3=\frac{100}{\pi}$

$r^3=31.83$

r=3.17 cm

Recall that:

$h=\frac{400}{\pi r^2}$

$h=\frac{400}{\pi *3.17^2}$

h=12.67cm

The dimensions of the can that will minimize the cost are a Radius of 3.17cm and a Height of 12.67cm.

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