Joan climbed down 330 feet to the bottom of a cave. Next, she climbed up 385 feet. What was her final elevation? Joan was

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

(1) Sixty million seventy-two is written

katovenus [111]

Standard form

im pretty sure

5 0

3 years ago

Read 2 more answers

A motorboat travels 204 kilometers in 6 hours going upstream. It travels 372 kilometers going downstream in the same amount of t

Arturiano [62]

9514 1404 393

Answer:

boat: 48 km/h
current: 14 km/h

Step-by-step explanation:

The upstream speed is ...

u = (204 km)/(6 h) = 34 km/h

The downstream speed is ...

d = (372 km)/(6 h) = 62 km/h

The speed of the boat in still water is the average of these values:

b = (34 kph +62 kph)/2 = 48 kph

The speed of the water is the difference between the boat's speed and the speed made good:

w = 48 -34 = 14 . . . km/h

The rate of the boat in still water is 48 km/h. The rate of the current is 14 km/h.

5 0

2 years ago

What’s 2 numbers that multiply to make -21 but add up to -4

irinina [24]

Answer:

2 numbers that multiply to make -21 = 3 x (-7)

2 numbers that add up to -4 = 3 - 7

Step-by-step explanation:

2 numbers that multiply to make -21 = 3 x (-7) = -21

2 numbers that add up to -4 = 3 - 7 = -4

4 0

3 years ago

The square of a certain negative number is equal to five more than one-half of that number. What is the number?

Goryan [66]

The answer is -2 yes das right

5 0

3 years ago