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2 years ago

The area of a quarter circle is 38.465 square inches. What is the quarter circle's radius?

Mathematics

1 answer:

LuckyWell [14K]2 years ago

3 0

The formula for a circle's area is $A=\pi r^2$ . We are given an area of 38.465 square inches for a quarter of it.

Multiply this value by 4 to compensate for the quarter circle.

$4 \times 38.465=\pi r^2$

$153.86=\pi r^2$

Divide both sides by pi (Note: I'm using the conventional value of 3.14)

$49=r^2$

Take the positive square root of both sides

$7=r$

The radius is 7 inches. Let me know if you have any questions, thanks!

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A street light is at the top of a 25 ft pole. A 4 ft tall girl walks along a straight path away from the pole with a speed of 6

Burka [1]

Answer:

Tip of the shadow of the girl is moving with a rate of 7.14 feet per sec.

Step-by-step explanation:

Given : In the figure attached, Length of girl EC = 4 ft

Length of street light AB = 25 ft

Girl is moving away from the light with a speed = 6 ft per sec.

To Find : Rate ( $\frac{dw}{dt}$ ) of the tip (D) of the girl's shadow (BD) moving away from th

light.

Solution : Let the distance of the girl from the street light is = x feet

Length of the shadow CD is = y feet

Therefore, $\frac{dx}{dt}=6$ feet per sec. [Given]

In the figure attached, ΔAFE and ΔADE are similar.

By the property of similar triangles,

$\frac{x}{21}=\frac{x+y}{25}$

25x = 21(x + y)

25x = 21x + 21y

25x - 21x = 21y

4x = 21y

y = $\frac{4x}{21}$

Now we take the derivative on both the sides,

$\frac{dy}{dt}=\frac{4}{21}\times \frac{dx}{dt}$

= $\frac{4}{21}\times 6$

= $\frac{8}{7}$

≈ 1.14 ft per sec.

Since w = x + y

Therefore, $\frac{dw}{dt}= \frac{dx}{dt}+\frac{dy}{dt}$

$\frac{dw}{dt}=6+1.14$

= 7.14 ft per sec.

Therefore, tip of the shadow of the girl is moving with a rate of 7.14 feet per sec.

3 0

3 years ago

300 is 10 times as much as what. please help me

Arlecino [84]

300 is 10 times as much as 30.
because if you do 30 x 10 you get 300

7 0

3 years ago

Read 2 more answers

What is 1/4 in feet?

Readme [11.4K]

Answer:

0.25 feet

7.62 centimeters

3 inches

Step-by-step explanation:

Not really a clear question-

6 0

2 years ago

Round to the nearest given place. 1.80431 thousandths

rodikova [14]

In order to round a number to the nearest thousandths, we have to check the number in the ten thousandths place:
1- If the number in the ten thousandths is less than 5, then the thousandths number will remain the same and all numbers after it will be converted to zeroes.
2- If the number in the ten thousandths is equal to or greater than 5, then the thousandths number will be incremented by 1 and all numbers after it will be converted to zeroes.

Applying this to the given number:
1.80431
The number in the ten thousandths position is 3 which is less than 5.
Therefore, rounding 1.80431 to the nearest thousandths will be:
1.80400 which is equivalent to 1.804

5 0

2 years ago

What is the inverse of y=x+3

taurus [48]

Answer: y3=x y 3 = x

Step-by-step explanation:

6 0

3 years ago