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Mama L [17]
3 years ago
8

Write an equation of the cosine function with amplitude pi/2 and period 3

Mathematics
1 answer:
juin [17]3 years ago
5 0

Answer:

y = \frac{\pi}{2}cos(\frac{2\pi}{3}x)

Step-by-step explanation:

Given

Amplitude = \frac{\pi}{2}

Period = 3

Required

Write the equivalent cosine function

The general formula is:

y = acos(bx)

Where

amplitude = |a|

period = \frac{2\pi}{b}

Substitute \frac{\pi}{2} for amplitude in amplitude = |a|

|a| = \frac{\pi}{2}

a = \frac{\pi}{2}

Substitute 3 for period in period = \frac{2\pi}{b}

\frac{2\pi}{b} = 3

<em>Multiply both sides by b</em>

2\pi = 3b

<em>Divide through by 3</em>

b = \frac{2\pi}{3}

Hence;

y = acos(bx) becomes

y = \frac{\pi}{2}cos(\frac{2\pi}{3}x)

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Answer:

Yes

Step-by-step explanation:

Yes, because each x has one specific y.

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3 years ago
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Set up a system of equations and then use your calculator to solve: In triangle ABC, the sum of angles and c is equal to three t
aalyn [17]

Answer:

Step-by-step explanation:

angle A = 40

angle B = 60

angle C = we don't know.

A + B + C = 180

C = 180 - A - B

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180 = 180...It checks!

4 0
3 years ago
What’s the area of this triangle?
tankabanditka [31]

Answer:

26.75

Step-by-step explanation:

There are two ways to do this. You can use the base*height/2 formula for the area of the triangle, or use the complex formula of determining triangle area without height.

The first is A=(b*h)/2

In this case you need to find the height using a²+b²=c²

Take your base (7.6) and divide it by 2 this will give you the bottom side of your triangle (3.8) now plug this, and the side value of 8 into the formula. Remember c is the hypotenuse (diagonal side) and x is the height.

3.8²+x²=8²

14.44+x²=64

x²=49.56

x=7.039 -now you have the height for the triangle and can use this to find the area

A=b*h (in this case we dont have to divide by two since we need two triangles because we split the original in two to find the base of 3.8)

so it's 3.8*7.039=26.75

(If you need more help look up Silicon Valley High school's video titled, "How to find the area of a triangle (without the height)"

It will teach you the formula A=\sqrt{s(s-a)(s-b)(s-c)} which teaches you to find the area of any triangle when all you are given is three sides

3 0
3 years ago
Joy Co. allocates overhead expenses to all departments on the basis of floor space (sq. ft.) occupied by each department. This y
salantis [7]
The ratio between the departments is

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15 : 18 : 9
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The budget needs to be divided into 5+6+3 = 14 parts
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The budget for department B is \frac{22000}{14}*6=9428.571428
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3 years ago
For what value of x is<br> 896Z15<br> 225 25<br> 11<br> XV14z? Assume z+0.
Karolina [17]

Answer: Value of x is, 8

Step-by-step explanation:  

Given:   ,.....[1]

To find the value of x:

Using exponent rules:

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or

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Simplify:

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5 0
3 years ago
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