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vazorg [7]
3 years ago
12

Sin^2(x/2)=sin^2x Find the value of x

Mathematics
1 answer:
Veronika [31]3 years ago
6 0
\sin^2\dfrac x2=\sin^2x
\dfrac{1-\cos x}2=1-\cos^2x
1-\cos x=2-2\cos^2x
2\cos^2x-\cos x-1=0
(2\cos x+1)(\cos x-1)=0
\implies\begin{cases}2\cos x+1=0\\\cos x-1=0\end{cases}\implies\begin{cases}\cos x=-\frac12\\\cos x=1\end{cases}

The first case occurs in 0\le x for x=\dfrac{2\pi}3 and x=\dfrac{4\pi}3. Extending the domain to account for all real x, we have this happening for x=\dfrac{2\pi}3+2n\pi and \dfrac{4\pi}3+2n\pi, where n\in\mathbb Z.

The second case occurs in 0\le x when x=0, and extending to all reals we have x=2n\pi for n\in\mathbb Z, i.e. any even multiple of \pi.
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For the population of all college students currently taking a statistics course, you want to estimate the proportion who are wom
inessss [21]

Answer:

No

Step-by-step explanation:

To estimate population proportion from a sample, we must ensure that the sample data is random. Though a simple random sample of college students from a particular college was used as the sample data. However, selection of the college should have been randomized as well, a stratified random sample would have been a better sampling method whereby certain colleges are selected based on region or other criteria and then a random sample of it's statistics students selected. The sample proportion Obtian from a sample of this nature will be more representative of the population proportion of all college statistic student.

5 0
3 years ago
Among 21- to 25-year-olds, 29% say they have driven while under the influence of alcohol. Suppose that three 21- to 25-year-olds
Sophie [7]

Answer:

P(3) = 0.0244

P(3) = 2.44%

the probability that all three selected have driven while under the influence of alcohol is 2.44% or 0.0244

Step-by-step explanation:

Given;

The probability that they have driven while under the influence of alcohol is;

P = 29% = 0.29

the probability that all three selected have driven while under the influence of alcohol is;

P(3) = P × P × P

P(3) = 0.29 × 0.29 × 0.29

P(3) = 0.024389

P(3) = 0.0244

P(3) = 2.44%

the probability that all three selected have driven while under the influence of alcohol is 2.44% or 0.0244

5 0
3 years ago
Help please 23 points will make brainliest
svlad2 [7]
It should be 78.54.
Double check that. 
Formula: V=πr2h/3
r2 is R squared 
8 0
3 years ago
When the point (-3,2) is reflected across the y-axis, what are the coordinates of the resulting point?
Elanso [62]
The new point would be at (3,2)
8 0
3 years ago
Read 2 more answers
HELP ME!!
inysia [295]

Answer:

y intercept (0,-2) x intercept (3,0)

Step-by-step explanation:

first we have to solve for y.

2x-3y=6

step 1 subtract 2x from each side

-3y=-2x+6

step 2 divide each side by -3

y=2/3x-2

now I am going to graph this to make it easier for you

5 0
2 years ago
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