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3 years ago

HURRY PLZ I NEED HELP This quarter circle has a radius of 7 centimeters.

Mathematics

2 answers:

Andrews [41]3 years ago

8 0

Answer: 38.47 is answer took test

Can I get brainliest pls

alina1380 [7]3 years ago

3 0

Answer:

r = 7 cm
C = 43.982297150257 cm
A = 153.9380400259 cm2

r = radius
C = circumference
A = area
π = pi = 3.1415926535898
√ = square root

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tester [92]

Answer:

The solutions on the given interval are :

$0$

$\pi$

$\cos^{-1}(\frac{1}{4})$

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Step-by-step explanation:

We will need the double angle identity $\sin(2x)=2\sin(x)\cos(x)$ .

Let's begin:

$2\sin(2x)=\sin(x)$

Use double angle identity mentioned on left hand side:

$2\cdot 2\sin(x)\cos(x)=\sin(x)$

Simplify a little bit on left side:

$4\sin(x)\cos(x)=\sin(x)$

Subtract $\sin(x)$ on both sides:

$4\sin(x)\cos(x)-\sin(x)=0$

Factor left hand side:

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Set both factors equal to 0 because at least of them has to be 0 in order for the equation to be true:

$\sin(x)=0 \text{ or } 4\cos(x)-1=0$

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$4\cos(x)-1=0$

Isolate $\cos(x)$ .

Add 1 on both sides:

$4 \cos(x)=1$

Divide both sides by 4:

$\cos(x)=\frac{1}{4}$

This is not as easy as finding on the unit circle.

We know $\arccos( )$ will render us a value between $0$ and $2\pi$ .

So one solution on the given interval for x is $x=\cos^{-1}(\frac{1}{4})$ .

We know cosine function is even.

So an equivalent equation is:

$\cos(-x)=\frac{1}{4}$

Apply $\cos^{-1}$ to both sides:

$-x=\cos^{-1}(\frac{1}{4})$

Multiply both sides by -1:

$x=-\cos^{-1}(\frac{1}{4})$

This going to be negative in the 4th quadrant but if we wrap around the unit circle, $2\pi$ , we will get an answer between $0$ and $2\pi$ .

So the solutions on the given interval are :

$0$

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