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4 years ago

12

If the diameter of a circle is 5 centimeters, how long is the arc subtended by an angle measuring 60 degrees

1 answer:

adell [148]4 years ago

7 0

2.618 cm

Step-by-step explanation:

The formulae for finding the length of an arc subtended by an angle at the center of the circle is;

∅/360 * 2πr

We can begin by finding the circumference of the circle;

π * D

= π * 5 = 15.708

We multiply by the fraction of the angle out of 360 degrees;

⁶⁰/ 360 = ¹/6

¹/6 * 15.708 = 2.618

= 2.618 cm

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Which polynomial is equal to (2x^2-5x-4)-(4x^2-3x-2) , and how is it equal?

Mademuasel [1]

Answer:

A. -2x^2-2x-2

Step-by-step explanation:

(2x^2-5x-4)-(4x^2-3x-2)

distribute the minus sign

(2x^2-5x-4)-4x^2+3x+2

2x^2-5x-4

-4x^2+3x+2

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-2x^2 -2x-2

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3 years ago

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Katen [24]

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3 years ago

How do I convert standard form to point slope

Fittoniya [83]

The point-slope form:

$y-y_1=m(x-x_1)$

$(x_1,\ y_1)$ - given point

$m$ - given slope

The standard form:

$Ax+By=C$

$y-y_1=m(x-x_1)$ <em>use distributive property</em>

$y-y_1=mx-mx_1$ <em>add $y_1$ to both sides</em>

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3 years ago

Find a unit vector that has the same direction as the given vector. 8i ? j + 4k

e-lub [12.9K]

Answer with Step-by-step explanation:

a.Let given vector

a=8i-j+4k

$\mid a\mid=\sqrt{(8)^2+(-1)^2+(4)^2}=9$

By using the formula

Magnitude of a vector= $\sqrt{x^2+y^2+z^2}$

Where x=Coefficient of i

y=Coefficient of j

z=Coefficient of k

Unit vector= $\hat{a}=\frac{a}{\mid a\mid}$

By using the formula

The unit vector= $\hat{a}=\frac{8i-j+4k}{9}=\frac{8}{9}i-\frac{1}{9}j+\frac{4}{9}k$

b.Let vector b=-2i+4j+2k

$\mid b\mid=\sqrt{(-2)^2+4^2+2^2}=2\sqrt 6$

$\hat{b}=\frac{-2i+4j+2k}{2\sqrt 6}$

Length of vector=6

Therefore, the vector in the direction of <-2,4,2> with length 6 is given by = $6\hat{b}=6\times \frac{-2i+4j+2k}{2\sqrt 6}$

The vector in the direction of <-2,4,2> with length 6 is given by = $-\sqrt 6(-i+2j+k)$

c. $\theta=\frac{\pi}{3}$

$\mid v\mid=8$

Let v= $v_x i+v_y j$

$v_x=\mid v\mid cos\theta$

$v_x=8cos\frac{\pi}{3}=8\times \frac{1}{2}=4$

$cos\frac{\pi}{3}=\frac{1}{2}$

$v_y=\mid v\mid sin\theta$

$v_y=8\times sin\frac{\pi}{3}=8\times \frac{\sqrt 3}{2}=4\sqrt 3$

$sin\frac{\pi}{3}=\frac{\sqrt 3}{2}$

Therefore, the vector v in component form= $4i+4\sqrt 3j$

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3 years ago

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Law Incorporation [45]

Answer:

$\bold{x = 34^\circ}$

Step-by-step explanation:

Given:

$cos x = sin (x + 22^\circ)$

To solve:

The given equation.

Solution:

First of all, let us consider an important property of sine and cosine.

$sin(90^\circ-\theta )=cos\theta$

OR

$cos(90^\circ-\theta )=sin\theta$

We can apply above property to solve for $x$ as per given equation.

$cos x = sin (x + 22^\circ)$

Changing $cosx$ to sine form:

$cosx=sin(90^\circ-x)$

$cosx=sin(90^\circ-x) = sin(x+22^\circ)$

$\therefore 90^\circ-x=x+22^\circ\\\Rightarrow 90^\circ-22^\circ=x+x\\\Rightarrow 2x=68^\circ\\\Rightarrow \bold{x = 34^\circ}$

So, solution to the equation $cos x = sin (x + 22^\circ)$ is:

$\bold{x = 34^\circ}$

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3 years ago