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3 years ago

In a circle, a 90° sector has an area of 36π in2. What is the radius of this circle?

Mathematics

2 answers:

34kurt3 years ago

6 0

Answer:

r = 12 in

Step-by-step explanation:

$A = \frac{1}{4} r^{2} \pi \\\\r = \sqrt{\frac{4A}{\pi } } = \sqrt{\frac{4 * 36\pi }{\pi } } = 2 * 6 = 12\ in$

mamaluj [8]3 years ago

4 0

Answer:

r = 12 in

Step-by-step explanation:

recall that a full circle is represented by a sector that is 360°

in our case, the given sector is 90°

Hence our sector is 90° / 360° = 1/4 of a circle

It is also given that our 90° sector (which we now know is 1/4 of a circle) has an area of 36π in² and recall that the area of a full circle is πr² (where r is the radius).

Hence,

πr² = 4 x area of 90° sector

πr² = 4 x 36π

πr² = 144π (divide both sides by π)

r² = 144

r = √144

r = 12 in

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Two automobiles start together from the same place and travel along the same route. The first averages 40 miles

natita [175]

Answer:

A. (55 x 5) - (40 x 5)

Step-by-step explanation:

You are solving how much miles (further along) would the second car be after 5 hours.

The first car averages 40 miles per hour. 5 hours later, it will have averaged about 200 miles in 5 hours (40 x 5 = 200).

The second car averages 55 miles per hour. 5 hours later, it will have averaged about 275 miles in 5 hours (55 x 5 = 275)

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3 years ago

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Drew has two cats. One cat weighs 17 pounds, and the other one weighs 12 1/2 pounds. Audrey’s dog weighs 33 pounds. What is the

Step2247 [10]

Answer: 3.5 pounds

Step-by-step explanation:

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3 years ago

12 grapes cost 90 $how many can bought in 40$

likoan [24]

Let x = the amount of grapes that can be bought for 0.40.

Note: By 90 I assume you mean 90 cents. The same for 40.

12/x = 0.90/0.40

0.90x = 12(0.40)

0.90x = 4.80

x = 4.80 ÷ 0.90

x = 5.33333

We can round the decimal to the ones place to get 5 grapes.

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3 years ago

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Find the slope and y-intercept of the line: y = 1/5 x - 8

Wewaii [24]

Answer:

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2 years ago

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If f(x) = 9x10 tan−1x, find f '(x).

djverab [1.8K]

Answer:

$\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + \frac{9x^{10}}{x^2 + 1}$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Product Rule]: $\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle f(x) = 9x^{10} \tan^{-1}(x)$

Step 2: Differentiate

[Function] Derivative Rule [Product Rule]: $\displaystyle f'(x) = \frac{d}{dx}[9x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]$
Rewrite [Derivative Property - Multiplied Constant]: $\displaystyle f'(x) = 9 \frac{d}{dx}[x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]$
Basic Power Rule: $\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]$
Arctrig Derivative: $\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + \frac{9x^{10}}{x^2 + 1}$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

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2 years ago