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3 years ago

Two angles are complementary. One angle mesurses 50 degrees. What is the measure of the other angle?

Mathematics

1 answer:

irina [24]3 years ago

6 0

Complimentary angles always equal 90° so the answer is C) 40°.

Hope this helps! :)

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Find the area of the region that lies inside the first curve and outside the second curve.

marishachu [46]

Answer:

Step-by-step explanation:

From the given information:

r = 10 cos( θ)

r = 5

We are to find the the area of the region that lies inside the first curve and outside the second curve.

The first thing we need to do is to determine the intersection of the points in these two curves.

To do that :

let equate the two parameters together

So;

10 cos( θ) = 5

cos( θ) = $\dfrac{1}{2}$

$\theta = -\dfrac{\pi}{3}, \ \ \dfrac{\pi}{3}$

Now, the area of the region that lies inside the first curve and outside the second curve can be determined by finding the integral . i.e

$A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} (10 \ cos \ \theta)^2 d \theta - \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \ 5^2 d \theta$

$A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} 100 \ cos^2 \ \theta d \theta - \dfrac{25}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \ d \theta$

$A = 50 \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix} \dfrac{cos \ 2 \theta +1}{2} \end {pmatrix} \ \ d \theta - \dfrac{25}{2} \begin {bmatrix} \theta \end {bmatrix}^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}}$

$A =\dfrac{ 50}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix} {cos \ 2 \theta +1} \end {pmatrix} \ \ d \theta - \dfrac{25}{2} \begin {bmatrix} \dfrac{\pi}{3} - (- \dfrac{\pi}{3} )\end {bmatrix}$

$A =25 \begin {bmatrix} \dfrac{sin2 \theta }{2} + \theta \end {bmatrix}^{\dfrac{\pi}{3}}_{\dfrac{\pi}{3}} \ \ - \dfrac{25}{2} \begin {bmatrix} \dfrac{2 \pi}{3} \end {bmatrix}$

$A =25 \begin {bmatrix} \dfrac{sin (\dfrac{2 \pi}{3} )}{2}+\dfrac{\pi}{3} - \dfrac{ sin (\dfrac{-2\pi}{3}) }{2}-(-\dfrac{\pi}{3}) \end {bmatrix} - \dfrac{25 \pi}{3}$

$A = 25 \begin{bmatrix} \dfrac{\dfrac{\sqrt{3}}{2} }{2} +\dfrac{\pi}{3} + \dfrac{\dfrac{\sqrt{3}}{2} }{2} + \dfrac{\pi}{3} \end {bmatrix}- \dfrac{ 25 \pi}{3}$

$A = 25 \begin{bmatrix} \dfrac{\sqrt{3}}{2 } +\dfrac{2 \pi}{3} \end {bmatrix}- \dfrac{ 25 \pi}{3}$

$A = \dfrac{25 \sqrt{3}}{2 } +\dfrac{25 \pi}{3}$

The diagrammatic expression showing the area of the region that lies inside the first curve and outside the second curve can be seen in the attached file below.

Download docx

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3 years ago

A convex quadrilateral with congruent diagonals is a ?

DaniilM [7]

Answer:

A rectangle is a quadrilateral that has congruent diagonals. The rectangle is a convex quadrilateral because of two diagonals which lie in the interior of the rectangle.

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3 years ago

3.16×10 tool the third power

Whitepunk [10]

The answer is 160 to this problem

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3 years ago

Determine whether each data set represents a function. Part A and B

Hitman42 [59]

Answer:

Part A - Represents a function

Part B - Doesn't represent a function.

Step-by-step explanation:

A set is just a list of numbers to check. The question is asking you based on the set...

(-5, 8)

(-6, 2)

(-2, -6)

(-1, 8)

(4,6)

if it is a valid function.

At NO point should a function have multiple x values. This fails the <em>Vertical Line Test</em> if visualized on a graph.

For Part A, there are no duplicate x values, meaning this function is valid.

For Part B, there is a duplicate x value - (2,9) & (2,4). Because of this, immediately the function is invalid. There can not be any duplicate x values in a valid function, <u>PERIOD</u>. If graphed, it fails the vertical line test.

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3 years ago

Which of the following trigonometric ratios has a value that is undefined?

masya89 [10]

Answer:

it is sin C

Step-by-step explanation:

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4 years ago