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3 years ago

Assuming that a 90° arc has an exact length of , find the length of the radius of the circle.

1 answer:

7 0

If the exact length is s, you have
.. s = r*θ . . . . θ = π/2
.. r = s/θ
.. r = 2s/π

Fill in the exact length for "s" in the formula and compute to find the radius.

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Is this answer correct?

34kurt

Answer:

Step-by-step explanation:

yes the answer is correct

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2 years ago

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Five times a number subtracted from 18 is triple the number find the number

Bess [88]

The number is 18

hope this helps

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3 years ago

PLEASE HELP! I'll give 5 out of 5 stars, give thanks, and give as many points as I can.

Liula [17]

Answer:

$\boxed{\boxed{x=\dfrac{\pi}{3}\ \vee\ x=\pi\ \vee\ x=\dfrac{5\pi}{3}}}$

Step-by-step explanation:

$\cos(3x)=-1\iff3x=\pi+2k\pi\qquad k\in\mathbb{Z}\\\\\text{divide both sides by 3}\\\\x=\dfrac{\pi}{3}+\dfrac{2k\pi}{3}\\\\x\in[0,\ 2\pi)$

$\text{for}\ k=0\to x=\dfrac{\pi}{3}+\dfrac{2(0)\pi}{3}=\dfrac{\pi}{3}+0=\boxed{\dfrac{\pi}{3}}\in[0,\ 2\pi)\\\\\text{for}\ k=1\to x=\dfrac{\pi}{3}+\dfrac{2(1)\pi}{3}=\dfrac{\pi}{3}+\dfrac{2\pi}{3}=\dfrac{3\pi}{3}=\boxed{\pi}\in[0,\ 2\pi)\\\\\text{for}\ k=2\to x=\dfrac{\pi}{3}+\dfrac{2(2)\pi}{3}=\dfrac{\pi}{3}+\dfrac{4\pi}{3}=\boxed{\dfrac{5\pi}{3}}\in[0,\ 2\pi)\\\\\text{for}\ k=3\to x=\dfrac{\pi}{3}+\dfrac{2(3)\pi}{3}=\dfrac{\pi}{3}+\dfrac{6\pi}{3}=\dfrac{7\pi}{3}\notin[0,\ 2\po)$

7 0

3 years ago

Read 2 more answers

Find two acute angles that satisfy the equation sin(2x + 7) = cos(x + 23). Check that your answers make

Vera_Pavlovna [14]

Answer:

The smaller angle is 43 and the larger angle is 47

Step-by-step explanation:

3 0

2 years ago

Divide the number 20 into two parts (not necessarily integers) in a way that makes the product of one part with the square of th

Ilya [14]

Answer:

13 1/3 and 6 2/3.

Step-by-step explanation:

Let the 2 parts be x and (20 - x).

So x^2(20 - x) must be a maximum.

y = x^2(20 - x)

y = 20x^2 - x^3

Finding the derivative):

y' = 40x - 3x^2 = 0 for maxm/minm value.

x( 40 - 3x) = 0

40 - 3x = 0

3x = 40

x = 40/3.

This is a maximum because the second derivative y" = 40 - 6x = 40 - 6(40/3)) is negative.

So the 2 numbers are 13 1/3 and 6 2/3.

3 0

2 years ago