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3 years ago

Find the area of the unshaded part of the figure

Mathematics

1 answer:

Tcecarenko [31]3 years ago

7 0

<h3>Answer:</h3>

unshaded area = 25(4 -π) in^2 ≈ 21.46 in^2

<h3>Step-by-step explanation:</h3>

Each of the shaded circles has a diameter of (20 in)/4 = 5 in, which also is the width of the enclosing rectangle. Then each circle has a radius of 2.5 in, and an area of ...

A = πr^2 = π(2.5 in)^2 = 6.25π in^2

The four circles together have an area of ...

4A = 4·(6.25π in^2) = 25π in^2

The area of the rectangle is the product of its length and width:

A = LW = (20 in)(5 in) = 100 in^2

Since the circles are shaded, the unshaded area is the difference between the rectangle area and the total area of the four circles:

unshaded area = (100 in^2) - (25π in^2) = 25(4 -π) in^2 ≈ 21.46 in^2

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3 years ago

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2 years ago

Joseph drives 125 miles in 2.5 hours. At the same rate, how far will he be able to travel in 6 hours

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Answer:

300

Step-by-step explanation:

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2 years ago

Using the exponential growth function for the U. S. population from 1970 through 2003:

jeka94

Answer:

Step-by-step explanation:

Using the exponential growth function for the U. S. population from 1970 through 2003:

A = 205.1e^0.011t

with the U.S. population being 205.1 million in 1970, when would the U. S. population reach 350 million?

2028

2048

2018

2038

We have the expression

A = 205.1e^0.011t

We are asked to find when would the U. S. population reach 350 million

A = 350

350 = 205.1e^0.011t

We divide both sides by 205.1

Divide both sides by 205.1

350/205.1 = 205.1e^0.011t/205.1

1.7064846416 = e^0.011t

We take the log of both sides

log 1.7064846416 = log e^0.011t

log 1.7064846416 = t log 0.011

t = log 1.7064846416/ log 0.011

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3 years ago

Consider a triangle with angles 30o-60o-90o, with hypotenuse of length 2. Calculate the lengths of the other 2 sides and store t

kumpel [21]

Answer:

1.00 and 1.73

Step-by-step explanation:

1) Calculating the 1st and the 2nd leg using trigonometric function sine:

$sin (30^{0})=\frac{c}{2}\Rightarrow \frac{1}{2}=\frac{c}{2}\Rightarrow 2*\frac{1}{2}=2*\frac{c}{2}\Rightarrow c=1\\sin(60^0)=\frac{b}{2}\Rightarrow \frac{\sqrt{3}}{2}=\frac{b}{2}\Rightarrow b=\sqrt{3}\Rightarrow\: b\approx \:1.73$

Once one leg is found there is another way to find the other leg, using Pythagorean Theorem too.

$a^{2}=b^{2}+c^{2}\Rightarrow 2^{2}=b^{2}+1^{2}\Rightarrow 4-1=b^{2}\Rightarrow b=\sqrt{3} b\approx 1.73$

Sides

a hypotenuse: 2.00

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b leg: 1.73

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c leg: 1.00

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3 years ago