Compare the following equations 568+29 over 6 and 568+29 over 3

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

7 months ago

Find the distance between the two points in simplest radical form. (-1, -5) and (4,7)

Neporo4naja [7]

Hope t will help u..........

6 0

2 years ago

Which statements are true for the following expression? 13 · (2 + 9)

Komok [63]

Answer:

13×11

143 ..

what are the statements?

8 0

2 years ago

The figure below shows a quadrilateral ABCD. Sides AB and DC are congruent and parallel: A quadrilateral ABCD is shown with the

algol [13]

A Quadrilateral A B C D in which Sides AB and DC are congruent and parallel.

The student has written the following explanation

Side AB is parallel to side DC so the alternate interior angles, angle ABD and angle BDC, are congruent. Side AB is equal to side DC and DB is the side common to triangles ABD and BCD. Therefore, the triangles ABD and CDB are congruent by SAS.

The student has also written

angles DBC and ADB are congruent and sides AD and BC are congruent. Angle DBC and angle ADB form a pair of alternate interior angles. Therefore, AD is congruent and parallel to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel.

Postulate SAS completely describes the student's proof.

Because if in a quadrilateral one pair of opposite sides are equal and parallel then it is a parallelogram.

6 0

2 years ago

Which of the following best approximates the value g(h(1))? A.-7 B.-5 C.0 D.2

Amiraneli [1.4K]

Answer:

Option (B)

Step-by-step explanation:

From the graph attached,

There are two functions graphed,

y = f(x) and y = h(x)

h(1) = 0 [Output value of function 'h' at the input value x = 1]

Since, g[h(1)] = g(0)

Therefore, value of function 'h' (output value) at (input value) x = 0,

g(0) = -5

Option B will be the correct option.

6 0

2 years ago