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UNO [17]
3 years ago
10

What is the amplitude, period, and phase shift of y= 5cos( x/2 + 2pi/3)

Mathematics
1 answer:
nordsb [41]3 years ago
3 0
Y = A cos(Bx + C)
A - amplitude
\frac{2\pi}{B} - period
- \frac{C}{B} - phase shift

y=5\cos{( \frac{x}{2} + \frac{2\pi}{3} )}
\\
\\y=5\cos{( \frac{1}{2}x + \frac{2\pi}{3})}
\\
\\A=5,B= \frac{1}{2},C= \frac{2\pi}{3}

Amplitude: 5
Period: \frac{2\pi}{B}=\frac{2\pi}{\frac{1}{2}}=4\pi
Phase shift: - \frac{C}{B} =- \frac{\frac{2\pi}{3}}{\frac{1}{2}}= -\frac{4\pi}{3}
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Answer:

Step-by-step explanation:

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3 0
3 years ago
Gwen volunteered to work at the ticket booth for her school's Halloween carnival. The chart below gives the number of hours Gwen
n200080 [17]

A linear relation is a relationship between two variables that when the corresponding pair of values of the variables are plotted, a straight line is obtained

The equation for the relationship between hours Gwen worked and number of tickets is <u> t = </u><u>15·h</u>

<u />

The reason the above equation is correct is as follows:

The given parameters are;

The table of values;

Hours(h): 1, 2, 3, 4

Tickets (t): 15, 30, 45, 60

Required: To write an equation that gives the relation between the number of hours Gwen worked and the number of tickets sold

Solution:

From the given table, we have;

The common difference between successive <em>h-values </em>is 1

The <em>common difference</em> between successive t<em>-values </em>is 30 - 15 = 45 - 30 = 60 - 45 = 15 = Constant

Given that the common difference of the <em>h</em>, and <em>t-values</em> are constant, the relationship is a linear relationship of the form, t = m·h + c

Where;

m = The rate of change of <em>t</em> with <em>h</em>, as follows;

m = (30 - 15)/(2 - 1) = 15

∴ t - 15 = 15 × (h - 1)

t - 15 = 15·h - 15

t = 15·h - 15 + 15 = 15·h

t = 15·h

The equation for the relation between the number of hours Gwen worked and the number of tickets she sold is<u> t = </u><u>15·h</u>

<u />

Learn more about mathematical relationships here:

brainly.com/question/10185505

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