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Mama L [17]
3 years ago
8

Write an equation of the cosine function with amplitude pi/2 and period 3

Mathematics
1 answer:
juin [17]3 years ago
5 0

Answer:

y = \frac{\pi}{2}cos(\frac{2\pi}{3}x)

Step-by-step explanation:

Given

Amplitude = \frac{\pi}{2}

Period = 3

Required

Write the equivalent cosine function

The general formula is:

y = acos(bx)

Where

amplitude = |a|

period = \frac{2\pi}{b}

Substitute \frac{\pi}{2} for amplitude in amplitude = |a|

|a| = \frac{\pi}{2}

a = \frac{\pi}{2}

Substitute 3 for period in period = \frac{2\pi}{b}

\frac{2\pi}{b} = 3

<em>Multiply both sides by b</em>

2\pi = 3b

<em>Divide through by 3</em>

b = \frac{2\pi}{3}

Hence;

y = acos(bx) becomes

y = \frac{\pi}{2}cos(\frac{2\pi}{3}x)

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Tim needs 23 3/4 m of wood trim to remodel a room. Wood trim is sold in lengths of 1 1/4 m. What equation can be used to find th
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I hope this helps you

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A leprechaun places a magic penny under a​ girl's pillow. The next night there are 2 magic pennies under her pillow. Each night
11Alexandr11 [23.1K]

Answer:

  • tn = 2097152 pennies
  • tn = 20971.52 dollars.

Step-by-step explanation:

A surprisingly large amount of money.

The question is "Does the amount of money just double or do the previous amounts add to the present amount?"

I think it just doubles. Not only that, but she can't spend any of it until night 22 is reached.

  • tn = a*2^(n - 1)
  • a = 1   She starts with 1 penny.
  • n = 22
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  • tn = 1*2^21
  • tn = 2097152 pennies
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8 0
3 years ago
The lines below are parallel. If the slope of the green line is -3, what is the
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Answer:-3

Step-by-step explanation:

The expression is already in decimal form.

−3 slope

8 0
2 years ago
An online ticket seller charges $44 for each ticket to a concert, plus a fixed handling fee of $12. Define the unknown variables
const2013 [10]

The unknown variables are how many tickets are being bought and the total.


t=tickets

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6 0
3 years ago
How do you solve this equation?
Travka [436]
Exponentail thingies

easy, look at all them them, see that they have 5 in common?
rremember how esay it was to factor
ax^2+bx+c=0

now we have
5^(2x)-6(5^x)+5=0
remember that 5^(2x)=(5^2)^x or (5^x)^2
in other words, we can rewrite it as
1(5^x)^2-6(5^x)+5=0
if yo want, replace 5^x with a and factor
1a^2-6a+5=0
(a-1)(a-5)=0
a=5^x
(5^x-1)(5^x-5)=0
set each to zero

5^x-1=0
5^x=1
take the log₅ of both sides
x=log₅1


5^x-4=0
5^x=4
take the log₅ of both sides
x=log₅4

x=log₅1 and/or log₅4







second quesiton

same thing

1(2^x)-10(2^x)+16=0
factor
(2^x-8)(2^x-2)=0
set each to zero

2^x-8=9
2^x=8
x=3

2^x-2=0
2^x=2
x=1

x=3 or 1







first one
x=log₅1 and/or log₅4
second one
x=1 and/or 3


7 0
3 years ago
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