What is one astronomical unit in inches

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

Which costs less to buy, a $1000 computer that is discounted 20% and then offered at an additional 10% off, or a $1000 computer

katen-ka-za [31]

A computer discounted at 30% off is less expensive.

First: 1000*.8 = 800
800*.9 = $720

Second: 1000*.7 = $700

6 0

3 years ago

Collins has a part-time job as a dog walker. The table below shows the amount of money Collins earned for different numbers of h

solmaris [256]

Answer:

Step-by-step explanation:

Part A:

For Dog walking, he earns $30 for 5 hours of work.

He earns $36 for 6 hours of work.

$30/5 hours = $6/hour

$36/6 hours = $6/hour

He earns $6/hour dog walking.

For 8 hours, he earns 8 hours * $6/hour = $48

To earn $66, he works 66/6 = 11 hours.

5 30

6 36

8 48

11 66

Part B:

He earns $7/hour for yard work, so multiply the number of hours by 7 to find the money he earns.

Table for yard work

Hours Money

5 $35

6 $42

8 $56

Part C:

For 5 hours, he earns $35 for yard work and $30 as a dog walker.

$35 - $30 = $5

8 0

2 years ago

John has taken out a loan for college. He started paying off the loan with a first payment of $100. Each month he pays, he wants

koban [17]

The infinite sequence of geometric terms is divergent if you try to add up all the terms. Sure the first 20 terms will add up to a fixed number but this isn't true for an infinite number of terms. The reason why the infinite series diverges is because r = 1.1 is larger than 1. If r > 1 then the infinite series diverges. It only converges if -1 < r < 1.

To write this in sigma notation, you would write $\displaystyle \sum_{n = 1}^{20}100(1.1)^{n-1}$ which is the result of adding the terms of 100(1.1)^(n-1) for n = 1 all the way up to n = 20. You can compute this by hand or preferably with a calculator or spreadsheet program