Find the equation of the line below

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

Ber [7]

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

3 0

1 year ago

What are the solutions of the equation x^3-x=0?

lana66690 [7]

Pi because pi can be any number, it could be 2 or 1299 or even 1000000 so that is why the answer to your question Nicolas is pi.

8 0

3 years ago

What is the area of a triangle with vertices (1,0) (5,0) (3,4)

Aleksandr-060686 [28]

Answer:

The area of the triangle is of 8 units of area.

Step-by-step explanation:

Answer:

The area of the triangle is of 21 units of area.

Step-by-step explanation:

The area of a triangle with three vertices $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ is given by the determinant of the following matrix:

$A = \pm 0.5 \left|\begin{array}{ccc}x_1&y_1&1\\x_2&y_2&1\\1_3&y_3&1\end{array}\right|$

In this question:

Vertices (1,0) (5,0) (3,4). So

$A = \pm 0.5 \left|\begin{array}{ccc}1&0&1\\5&0&1\\3&4&1\end{array}\right|$

$A = \pm 0.5(1*0*1+0*1*3+1*5*4-1*0*3-0*5*1-1*1*4)$

$A = \pm 0.5*(20-4)$

$A = \pm 0.5*16 = 8$

The area of the triangle is of 8 units of area.

3 0

3 years ago

A surgery asks 25 people if they prefer brand A of brand B laundry detergent. The data show that 12 people prefer brand A. Write

SVETLANKA909090 [29]

Answer:

13 to 25

13:25

$\frac{13}{25}$

Step-by-step explanation:

All of these show the ratio 13/25

Hope this helps!

8 0

3 years ago

Need help with trig!

dedylja [7]

Answer:

1. A. $4.42$

2. F. $20.9$

3. G. $4.57$

4. A. $4.50$

Step-by-step explanation:

5 0

3 years ago

Find the equation of the line below￼

Find the equation of the line below