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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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What is the answer?​
charle [14.2K]

Answer:

x = 20 but see below.

Step-by-step explanation:

Remark.

This is not well enough marked to know whether D = A or whether you have to do some algebra to find the relationship between A and D. So I will assume A = D and then I'll solve it so you have to manipulate A and D.

A = D

3x - 10 = 2x + 10                     Add 10 to both sides

3x - 10 + 10 = 2x + 10 + 10     Cancel

3x = 2x + 20                           Subtract 2x from both sides

3x-2x=2x-2x + 20

x = 20

A = E

If A = E then to find x you have to add 3 angles together.

E + D + 45 = 180                  Add the three angles of the triangle

E + D = 180 - 45                  Subtract  45 from both sides

E + D = 135                          Substitute for D and E

3x - 10 + 2x + 10 = 135        Combine like terms

5x = 135                              Divide by 5

x = 135 / 5

x = 27

Answer

I'd go with the first one.

5 0
3 years ago
Find the 2nd term of (2x+3y)^3
puteri [66]

Answer:

The 2nd term is 3y

Step-by-step explanation:

2x +       3y

__          __

1            2

term     term

5 0
2 years ago
Read 2 more answers
How can you find this distance (-3,7),(0,4) in words
Bezzdna [24]

Answer:

The distance between these two given points is:

3\sqrt{2}

Step-by-step explanation:

We are given two points:

(-3,7),(0,4)

<em>The distance between two points (a,b) and (c,d) is given by the distance formula as:</em>

<em>\sqrt{(c-a)^2+(d-b)^2</em>

similarly we can find the length of a line segment by considering the distance between the end points of the line segment.

So here (a,b)=(-3,7)

and (c,d)=(0,4).

Hence distance between these two points is given by:

\sqrt{(0-(-3))^2+(4-7)^2}=\sqrt{(3)^2+(-3)^2}=\sqrt{9+9}\\   \\=\sqrt{18} \\\\=3\sqrt{2}

6 0
3 years ago
Read 2 more answers
Please solve each equation &amp; check your solution. Thank You!
Deffense [45]

Answer:

G). 1.2x + 7.92 -3.3x = 41

-2.1x=33.08

x = 33.08/-2.1

x = - 15.752

H). 3x/2 + 9/5 = 12

Multiply through by 10

15x + 18 =120

15x =120-18

15x = 102

x =102/15

x=34/5

I). 5 = 9/4 - r/3

Multiply through by 12

60= 27 - 4r

60 - 27 = -4r

33 = - 4r

r = -33/4

J). 2(x - 2) = 12

2x - 4 = 12

2x = 16

x = 16/2

x = 8

8 0
3 years ago
A graduate-level computer science course only gives the grades of A, B, or C. The department has determined that there should be
kupik [55]

Step-by-step explanation:

The null hypothesis: The department has determined that there should be 40% A’s given, 40% B’s given and 20% C’s given as final grades for the course

If  the p-value for this hypothesis test is = 0.000... and this number is lower than the 0.05 significance level, we reject the null hypothesis and conclude that from the result of our observation that final grades do not match this grading guidelines.

It means the grading guidelines was exceeded in terms of As, was  less in terms of Bs and was higher in terms of Cs i e the grading guidelines was not consistent with what was stated in the null.

6 0
2 years ago
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