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tensa zangetsu [6.8K]
2 years ago
10

What is the angle, in degrees, if the Area is 180 square miles and the radius is 42,240 feet?

Mathematics
1 answer:
Savatey [412]2 years ago
5 0

Step-by-step explanation:

the area of a circle (all 360°) is

pi×r²

with r being the radius.

the area of a circle segment is just the corresponding fraction of the whole circle.

so the area of a segment of x degrees is

pi×r² × x/360

in our case we know

pi×42240² × x/360 = 180 mi²

we also know that there are 5280 ft in 1 mile.

so, the radius is actually

42240 / 5280 = 8 miles

and therefore our equation resulting in mi² has to use miles and not ft and has to look that way :

pi×8² × x/360 = 180 mi²

pi×64 × x/360 = 180

pi×64 × x = 180×360

pi×x = 180×360/64 = 1012.5

x = 1012.5/pi = 322.2887598...°

so, the angle of the segment of a circle with the area of 180 mi² and the radius of 8 mi is 322.2887598...°

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What is the value of y?
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Answer:

y = 226°

Step-by-step explanation:

Circle Geometry Theorem: Angle at the centre of a circle is twice the size of the angle at the circumference.

113° × 2 = y

226° = y

4 0
3 years ago
Anna, Boris, and Clara thought of 1 number each Ana's number increased by 20 is 21 greater than boris's number decreased by 22.
sleet_krkn [62]

Answer:

Clara's number is 42 less than Anna's number

Step-by-step explanation:

We can start this problem out by setting our variables up:

A= Anna's number

B= Boris's number

C= Clara's number

so we can use them to build our equations. We can sepparate the problem into little more understandable pieces of information, let's start with the first piece of information:

- "Ana's number increased by 20"

A+20

- "boris's number decreased by 22"

B-22

- "21 greater than boris's number decreased by 22."

(B-22)+21

- "Ana's number increased by 20 is 21 greater than boris's number decreased by 22."

A+20=(B-22)+21

This is our first important equation here. Let's go with the second part of the problem:

- "Boris's number decreased by 20"

B-20

- "claras number increased by 22"

C+22

- "21 greater than claras number increased by 22"

(C+22)+21

Now the whole thing:

"Boris's number decreased by 20 is 21 greater than claras number increased by 22."

B-20=(C+22)+21

This is our second important equation.

So now we have the following system of equations:

A+20=(B-22)+21

B-20=(C+22)+21

We can now simplify the equations by combining like terms so we get:

Equation 1:

A+20=(B-22)+21

we can get rid of the parenthesis so we get:

A+20=B-22+21

We can subtract a 20 from both sides of the equation so we get:

A=B-22+21-20

We perform the subtractions so we get:

A=B-21

Equation 2:

B-20=(C+22)+21

We get rid of the parenthesis:

B-20=C+22+21

We add a 20 to both sides so we get:

B=C+22+21+20

We can now perform the additions so we get:

B=C+63

And now we can combine the equations. In this case we can substitute equation 2 into equation 1 to get:

A=C+63-21

We combine like terms to get:

A=C+42

We can subtract 42 from both sides to get:

C=A-42

which reads:

Clara's number is 42 less than Anna's number.

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Each year farmer records the number of pumpkins he sold for 5 weeks. The mean is 782 and the mean absolute deviation is 52. List
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Answer:

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