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3 years ago

Use a double angle or half angle identity to find the exact value of each expression

Mathematics

1 answer:

inna [77]3 years ago

4 0

θ is given to be in the fourth quadrant (270° < θ < 360°) for which sin(θ) < 0 and cos(θ) > 0. This means

cos²(θ) + sin²(θ) = 1 ==> sin(θ) = -√[1 - cos²(θ)] = -3/5

Now recall the double angle identity for sine:

sin(2θ) = 2 sin(θ) cos(θ)

==> sin(2θ) = 2 (-3/5) (4/5) = -24/25

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The solution for the system equations 8x-6y=-32 and -8x+5y=36

Ghella [55]

Answer:

x=47, y=68

Step-by-step explanation:

Add the two equations. Then we get

-y=-68

y=68

Substituting the value of y in the first equation,

8x-6(68)=-32

8x-408=-32

8x=376

x=47

6 0

3 years ago

The steepest part of any walking trail in Craters of the Moon National Monument rises 9 yards vertically for every 50 yards trav

pogonyaev

Answer:

4.5

Step-by-step explanation:

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2 years ago

This rectangular patio is tiled using 50 cm by 50 cm square tiles. How many tiles are used?

Bad White [126]

Answer:

60 tiles are used

Step-by-step explanation:

1m equals 100 cm.

5m equals 500

3m equals 300

the whole thing is 500 by 300 which when you multiply gives you

150,000. When you multiple 50 by 50 it gives you 2,500. So when you divide 150,000 by 2,500 it gives you a total of 60 tiles. HOPE THIS HELPS

5 0

3 years ago

Read 2 more answers

Semicircles and quarter circles are types of arc lengths. Recall that an arc is simply part of a circle. We learned about the de

attashe74 [19]

The question is incomplete. Here is the complete question.

Semicircles and quarter circles are types of arc lengths. Recall that an arc is simply part of a circle. we learned about the degree measure of an ac, but they also have physical lengths.

a) Determine the arc length to the nearest tenth of an inch.

b) Explain why the following proportion would solve for the length of AC below: $\frac{x}{12\pi } = \frac{130}{360}$

c) Solve the proportion in (b) to find the length of AC to the nearest tenth of an inch.

Note: The image in the attachment shows the arc to solve this question.

Answer: a) 9.4 in

c) x = 13.6 in

Step-by-step explanation:

a) $\frac{arclength}{2\pi.r } = \frac{mAB}{360}$ , where:

r is the radius of the circumference

mAB is the angle of the arc

arc length = $\frac{mAB.2.\pi.r }{360}$

arc length = $\frac{90.2.3.14.6}{360}$

arc length = 9.4

The arc lenght for the image is 9.4 inches.

b) An arc length is a fraction of the circumference of a circle. To determine the arc length, the ratio of the length of an arc to the circumference is equal to the ratio of the measure of the arc to 360°. So, suppose the arc length is x, for the arc in (b):

$\frac{x}{2.6.\pi } = \frac{130}{360}$