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Verizon [17]
3 years ago
8

Solve sin x - (3sin x-1) = 0

Mathematics
1 answer:
soldi70 [24.7K]3 years ago
3 0

Answer:

\large\boxed{x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi,\ k\in\mathbb{Z}}

Step-by-step explanation:

\sin x-(3\sin x-1)=0\\\\\sin x-3\sin x+1=0\qquad\text{subtract 1 from both sides}\\\\-2\sin x=-1\qquad\text{divide both sides by 2}\\\\\sin x=\dfrac{1}{2}\Rightarrow x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi,\ k\in\mathbb{Z}

\text{Equation:}\\\\\sin x=a\\\\\text{has solutions}\\\\x=\theta+2k\pi\ \vee\ x=(\pi-\theta)+2k\pi\\\\\text{Why}\ 2k\pi?\\\text{Because the sine function has a period of}\ 2\pi.

\text{look at the table}\\\\\sin x=\dfrac{1}{2}\to x=\dfrac{\pi}{6}\ \vee\ x=\pi-\dfrac{\pi}{6}=\dfrac{5\pi}{6}

\text{Other solution:}\\\\\sin x=\dfrac{1}{2}\Rightarrow x=\sin^{-1}\dfrac{1}{2}\\\\x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi

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798/6 hours

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Answer:

a. (29526.192 , 32155.808)

b. (29673.9301 , 32008.0699)

Step-by-step explanation:

on calculation, we find that sample mean = 30843 and sample standard deviation = 3018.504, and n=20

1)

Sample Mean = 30841

SD = 3000

Sample Size (n) = 20

Standard Error (SE) = SD/root(n) = 670.8204

alpha (a) = 1 - 0.95 = 0.05

z critical value for 95% confidence interval:

z(a/2) = z(0.025) = 1.96

Margin of Error (ME) = z(a/2) x SE = 1314.808

95% confidence interval is given by:

Sample Mean +/- (Margin of Error) = 30841 +/- 1314.808

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2)when std dev of population is not known, we use sample's, but we have to use t instead of z

Sample Mean = 30841

SD = 3018.504

Sample Size (n) = 20

Standard Error (SE) = SD/root(n) = 674.958

alpha (a) = 1-0.9 = 0.1

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t(a/2, n-1 ) = 1.7291

Margin of Error (ME) = t(a/2,n-1)x SE = 1167.0699

90% confidence interval is given by:

Sample Mean +/- (Margin of Error)

30841 +/- 1167.0699 = (29673.9301 , 32008.0699)

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