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igomit [66]
1 year 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]1 year 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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Step-by-step explanation:

Teri bought 360 rubber band to make a bracelet

  • 15% of the bands were white and the rest were red
  • After using 140 bands to make her 1st bracelet , 20% of the remaining bands were white

We need to find how many red bands did Teri use on the 1st bracelet

∵ Teri bought 360 rubber bands

∵ 15% of the bands were white

- Find the number of white bands by multiplying 155 by 360

∴ The number of the white bands = 15% × 360

∵ 155 = 15 ÷ 100 = 0.15

∴ The number of the white bands = 0.15 × 360 = 54

∵ She used 140 bands to make the first bracelet

∴ The remaining band = 360 - 140 = 220

∵ 20% of the remaining bands were white

- Find the number remaining white bands by multiplying 20% by 220

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∴ The number of red bands in the 1st bracelet = 140 - 10 = 130

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Learn more:

You can learn more about the word problems in brainly.com/question/10557938

#LearnwithBrainly

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