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3 years ago

Find the area of the shaded region. Round your answer to the nearest hundredth.

Mathematics

1 answer:

Alborosie3 years ago

7 0

Answer:

Step-by-step explanation:

The formula for finding the area of a pentagon(regular) given 1 side is

A = $\frac{1}{4}\sqrt{5(5+2\sqrt{5})}s^{2}\)$

s (the side) = 12

Area = $\frac{1}{4}\sqrt{5(5+2\sqrt{5})}12^{2}\)$

Area = $\frac{1}{4}\sqrt{5(5+2\sqrt{5})}144\)$

Area = sqrt(5(5 + 2*2.2361) * 36

Area = sqrt(5( 5 + 4.4721)) * 36

Area = sqrt(5*9.4721) * 36

Area = sqrt(47.3606) * 36

Area = 6.882 * 36

Area = 247.7485

The area of the circle = pi r*2 but we don't have r.

If you know any trig, the formula for the radius of the circle is

R = s/(2*sin(180)/n) n = 5 because you are using a 5 sided figure.

R = 12/(2*sin(180/5)

R = 12/2* sin(36)

R = 6 / sin(36)

R = 10.207

So the area of the circle is pi * R^2

Area = 3.14 * 10.2078^2

Area = 327.1854

The area of the shaded part is the difference between the 2 areas we found

Answer: 327.1854 - 247.7485

Answer: 79.44

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You are planning to invest $5000 in an account earning 9% per year for retirement. a. If you put the $5000 in an account at age

ICE Princess25 [194]

Answer:

A).Amount = $218250

B). Amount = $88700

Step-by-step explanation:

A) .$5000 in an account at age 23, and withdraw it 42 years

Number of years t= 42 years

Principal P = $5000

Rate r= 9%

Number of times compounded n= 42

A= p(1+r/n)^(nt)

A= 5000(1+0.09/42)^(42*42)

A= 5000(1+0.002143)^(1764)

A= 5000(1.002143)^1764

A= 5000(43.65)

A= 218250

Amount = $218250

B).waits 10 years before making the deposit, so that it stays in the account for only 32 years

Number of years t= 32 years

Principal P = $5000

Rate r= 9%

Number of times compounded n= 32

A= p(1+r/n)^(nt)

A= 5000(1+0.09/32)^(32*32)

A= A= 5000(1+0.0028125)^(1024)

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5 0

3 years ago

39/250 in simplest form

OleMash [197]

Getting the simplest form of a fraction is the same with getting its lowest term. Reducing fractions to its lowest term is a very simple thing to do. Here's how to simplify fractions:

There are two ways in simplifying fractions. The first method is to equally divide both numerator and denominator which results to only whole numbers. Getting the GCF (Greatest Common Factor) or GCD (Greatest Common Divisor) is the second method.

As to the fraction above, 39/250, the second method is applicable.
Let us get the GCF of 39 and 250
39= 1,3,13,39
250= 1, 2, 5, 10, 25, 50, 125, 250

Therefore, the GCF of 39 and 250 is 1. We can conclude then that 39/250 is already on its simplest form thus;
39 ÷ 1 is equal to 39
250 1 250

7 0

3 years ago

Finding Derivatives Implicity In Exercise, find dy/dx implicity. 4x3 + ln y2 + 2y = 2x

lisov135 [29]

Answer:

$\frac{dy}{dx}=\frac{y(1-6x^2)}{(1+y)}$

Step-by-step explanation:

Given function : 4x³ + ln(y²) + 2y = 2x

on differentiating both sides with respect to 'x', we get

$\frac{d(4x^3 + ln(y^2) + 2y)}{dx}= \frac{d(2x)}{dx}$

$12x^2+\frac{2}{y}(\frac{dy}{dx})+2(\frac{dy}{dx})=2$

$12x^2+(\frac{2}{y}+2)\frac{dy}{dx}=2$

$(\frac{2+2y}{y})\frac{dy}{dx}=2-12x^2$

$\frac{dy}{dx}=\frac{y(2-12x^2)}{2+2y}$

$\frac{dy}{dx}=\frac{2y(1-6x^2)}{2(1+y)}$

$\frac{dy}{dx}=\frac{y(1-6x^2)}{(1+y)}$

3 0

3 years ago

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Marizza181 [45]

Answer:

Step-by-step explanation:

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