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igomit [66]
11 months ago
15

Lesson: 1.08Given this function: f(x) = 4 cos(TTX) + 1Find the following and be sure to show work for period, maximum, and minim

um:Period =Equation of the mideline:Maximum =Minimum =
Mathematics
1 answer:
Ber [7]11 months ago
3 0

The given function is

f(x)=4\cos \text{(}\pi x)+1

The general form of the cosine function is

y=a\cos (bx+c)+d

a is the amplitude

2pi/b is the period

c is the phase shift

d is the vertical shift

By comparing the two functions

a = 4

b = pi

c = 0

d = 1

Then its period is

\begin{gathered} \text{Period}=\frac{2\pi}{\pi} \\ \text{Period}=2 \end{gathered}

The equation of the midline is

y_{ml}=\frac{y_{\max }+y_{\min }}{2}

Since the maximum is at the greatest value of cos, which is 1, then

\begin{gathered} y_{\max }=4(1)+1 \\ y_{\max }=5 \end{gathered}

Since the minimum is at the smallest value of cos, which is -1, then

\begin{gathered} y_{\min }=4(-1)+1 \\ y_{\min }=-4+1 \\ y_{\min }=-3 \end{gathered}

Then substitute them in the equation of the midline

\begin{gathered} y_{ml}=\frac{5+(-3)}{2} \\ y_{ml}=\frac{2}{2} \\ y_{ml}=1 \end{gathered}

The answers are:

Period = 2

Equation of the midline is y = 1

Maximum = 5

Minimum = -3

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3 years ago
Which expression correctly represents “six more than the product of five and a number, decreased by one”?
Nataly_w [17]

Answer:

Step-by-step explanation:

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Finally, "six more than the product of 5 and a number, decreased by one" would be

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7 0
3 years ago
Which relations are functions? List the relation number(s) that are function(s) in the answer bank
Sergeu [11.5K]

Answer:

options 1,3,4 are functions.

Step-by-step explanation:

RULE: a relation is said to be a function if every element in the domain ( the numbers in the left side in the below sets) is related to only one number ( number on the right side in the below sets).

Let us check each option one by one:

1.   3           2

    9           1

   -4           7

    0          -2

here each number on the left side is mapped to or is related to one number only.

so this relation is a function

2.  7         1

    -5        2,3

     1         0

here, "-5" is mapped to two different numbers. so this relation is not a function.

3.  -2    -4

    2      4

    6      8

    -6    -8

here each number on the left side is mapped to or is related to one number only.

so this relation is a function

4.  1     3

   -1    3

   2    3

  -2    3

here each number on the left side is mapped to or is related to one number only.

so this relation is a function.

even if it is related to the same number, it doesn't matter.

it should follow the above given rule that's it.

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3 years ago
Which is higher 214.7 or 214.275
Lostsunrise [7]

easy 214.7 because if it was rounded it would be 214.700 an this is way bigger than 214.275

8 0
3 years ago
I need help i need to simplify 7(2y+1)+3y
Artist 52 [7]

Simplified form : 17y + 7

5 0
3 years ago
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