So a general harmonic equation is Asin(2πt/T). Little t is just a variable. 6 inches is the height of one maximum and one minimum from equilibrium, so that is the amplitude A. T is the period, or the time of one cycle (or wavelength), which is 2 seconds.
The equation is therefore (in terms of seconds and inches), 6*sin(2πt/2), or 6*sin(πt).
Answer:
27 chickens
Step-by-step explanation:
A chicken farmer also has cows for a total of 30 animals
Both animals have a total of 66 legs
Let a represent the number of chicken
Let b represent the number of cows
a + b= 30........equation 1
Since a chicken has only two legs and a cow has four leg then, the expression can be represented as
2a + 4b= 66........equation 2
From equation 1
a + b= 30
a = 30-b
Substitute 30-b for a in equation 2
2a + 4b= 66
2(30-b) + 4b= 66
60 - 2b + 4b= 66
60 + 2b= 66
2b= 66-60
2b= 6
b= 6/2
b= 3
Substitute 3 for b in equation 1
a + b = 30
a + 3=30
a= 30-3
a= 27
Hence the farmer has 27 chickens
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Information Given:
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ON = 7x - 9
LM = 6x + 4
MN = x - 7
OL = 2y - 7
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Since it is a parallelogram:
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ON = LM and
MN = OL
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ON = LM:
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7x - 9 = 6x + 4
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Subtract 6x from both sides:
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x - 9 = 4
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Add 9 to both sides:
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x = 13
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MN = OL:
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x - 7 = 2y - 7
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Sub x = 13:
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13 - 7 = 2y - 7
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Simplify:
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6 = 2y - 7
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Add 7 on both sides:
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13 = 2y
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Divide by 2:
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y = 13/2
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Answer: x = 13, y = 13/2 (Answer D)
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Answer:
$252.5
Step-by-step explanation:
45(4.5)+50
202.5+50
=252.5
well, let's first notice, all our dimensions or measures must be using the same unit, so could convert the height to liters or the liters to centimeters, well hmm let's convert the volume of 1000 litres to cubic centimeters, keeping in mind that there are 1000 cm³ in 1 litre.
well, 1000 * 1000 = 1,000,000 cm³, so that's 1000 litres.
![\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=1000000~cm^3\\ h=224~cm \end{cases}\implies \stackrel{cm^3}{1000000}=\pi r^2(\stackrel{cm}{224}) \\\\\\ \cfrac{1000000}{224\pi }=r^2\implies \sqrt{\cfrac{1000000}{224\pi }}=r\implies \cfrac{1000}{\sqrt{224\pi }}=r\implies \stackrel{cm}{37.7}\approx r](https://tex.z-dn.net/?f=%5Ctextit%7Bvolume%20of%20a%20cylinder%7D%5C%5C%5C%5C%20V%3D%5Cpi%20r%5E2%20h~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%20h%3Dheight%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20V%3D1000000~cm%5E3%5C%5C%20h%3D224~cm%20%5Cend%7Bcases%7D%5Cimplies%20%5Cstackrel%7Bcm%5E3%7D%7B1000000%7D%3D%5Cpi%20r%5E2%28%5Cstackrel%7Bcm%7D%7B224%7D%29%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B1000000%7D%7B224%5Cpi%20%7D%3Dr%5E2%5Cimplies%20%5Csqrt%7B%5Ccfrac%7B1000000%7D%7B224%5Cpi%20%7D%7D%3Dr%5Cimplies%20%5Ccfrac%7B1000%7D%7B%5Csqrt%7B224%5Cpi%20%7D%7D%3Dr%5Cimplies%20%5Cstackrel%7Bcm%7D%7B37.7%7D%5Capprox%20r)
now, we could have included the "cm³ and cm" units for the volume as well as the height in the calculations, and their simplication will have been just the "cm" anyway.
