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Dmitry [639]
3 years ago
7

What is the measure of ∠P, to the nearest degree?

Mathematics
1 answer:
melamori03 [73]3 years ago
6 0
By the Law of Sines
   sin(P)/MN = sin(N)/MP
   sin(P) = MN*sin(N)/MP
   ∠P = arcsin(34*sin(78°)/46) ≈ arcsin(0.722979)
   ∠P ≈ 46.30°

The measure of ∠P to the nearest degree is 46°.


_____
This measure is confirmed by drawing it using a geometry program.

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which of the following is a solution of 2cos^2x-cost-1=0 a. 0 degrees b. 150 degrees c. 180 degrees d. 210 degrees
Luba_88 [7]

Answer:

{0, 150} degrees

Step-by-step explanation:

Given 2cos^2x-cost-1=0, let's simplify this problem by temporarily replacing cos x with y:

2y^2 - y -1 = 0

This can be solved by factoring:  (2y + 1)(y - 1) = 0.  From this we get two solutions:  y = -1/2 and y = 1.

Remembering that we let y = cos x, we now solve:

cos x = -1/2 and cos x = 1.

Note that cos x = 1 when x = 0 and the "adjacent side" coincides with the hypotenuse.

cos x = -1/2 when the hypotenuse is 2 and the "adjacent side" is -1.  This has two solutions between 0 and 360 degrees:  150 degrees and  270 degrees.

Four answer choices are given.  Both (a) (0 degrees) and (b) (150 degrees) satisfy the original equation.  Thus, the solution set is {0, 150} (degrees).

3 0
3 years ago
Find the x and the area of the shape perimeter is 64.5​
Umnica [9.8K]

Answer:

x=8

A = 192

Step-by-step explanation:

The perimeter is the sum of the outer lengths

17.9 + 22.6 + 3x = 64.5

Combine like terms

40.5 +3x = 64.5

Subtract 40.5 from each side

40.5 +3x -40.5 = 64.5 - 40.5

3x =24

Divide each side by 3

3x/3 = 24/3

x = 8

The area of a triangle is given by

A = 1/2 bh

The base is 3x = 3(8) =24

and the height is 2x = 2(8) =16

A = 1/2 (24) * 16

A =192

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3 years ago
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mariarad [96]
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3 years ago
Show work<br> Find the volume of the pyramid
Burka [1]
<u></u><em>Hello there, and thank you for posting your question here on brainly.

______________________________________________________________
Answer: 128
</em>
<em>Why?
</em><em>______________________________________________________________
To find the volume of a cylinder, we have to use the formula lwh/3. The length is 8, width is 4, and height is 12. So we have to multiply all of those together, then divide by 3. (8 * 4 = 32) -> (32 * 12 = 384) -> (384/3 = 128) The volume is 128.

</em>
<em>Hope this helped you! ♥</em><em>
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3 0
3 years ago
Please answer as well?
dimulka [17.4K]

Answer:

I think it is the 3rd one

Step-by-step explanation:

I hope it is. Sorry if not, I tried.

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