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Reptile [31]
4 years ago
14

What is 1-2sin^2x=sinx Please show steps and find all solutions in interval [0,2pi)

Mathematics
1 answer:
Svetlanka [38]4 years ago
4 0

Answer:

\large\boxed{x=\dfrac{3\pi}{2}\ \vee\ x=\dfrac{\pi}{6}\ \vee\ x=\dfrac{5\pi}{6}}

Step-by-step explanation:

1-2\sin^2x=\sin x\\\\\text{substitute}\ t=\sin x,\ t\in[-1,\ 1]\\\\1-2t^2=t\qquad\text{subtract t from both sides}\\\\-2t^2-t+1=0\qquad\text{change the signs}\\\\2t^2+t-1=0\\\\2t^2+2t-t-1=0\\\\2t(t+1)-1(t+1)=0\\\\(t+1)(2t-1)=0\iff t+1=0\ \vee\ 2t-1=0\\\\t+1=0\qquad\text{subtract 1 from both sides}\\\boxed{t=-1}\\\\2t-1=0\qquad\text{add 1 to both sides}\\2t=1\qquad\text{divide both sides by 2}\\\boxed{t=\dfrac{1}{2}}

\sin x=-1\to x=-\dfrac{\pi}{2}+2k\pi,\ k\in\mathbb{Z}\\\\\sin x=\dfrac{1}{2}\to x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi,\ k\in\mathbb{Z}\\\\x\in[0,\ 2\pi)

x=-\dfrac{\pi}{2}\notin[0,\ 2\pi)\\\\x=-\dfrac{\pi}{2}+2\pi=\dfrac{3\pi}{2}\in[0,\ 2\pi)\\\\x=-\dfrac{\pi}{2}+4\pi=\dfrac{7\pi}{2}\notin[0,\ 2\pi)\\\\x=\dfrac{\pi}{6}\in[0,\ 2\pi)\\\\x=\dfrac{\pi}{6}+2\pi=\dfrac{13\pi}{6}\notin[0,\ 2\pi)\\\\x=\dfrac{5\pi}{6}\in[0,\ 2\pi)\\\\x=\dfrac{5\pi}{6}+2\pi=\dfrac{17\pi}{6}\notin[0,\ 2\pi)

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The probability of rain on the last day of July is 95 % . If the probability remains constant for the first seven days of August
8090 [49]

The probability that it rains at most 2 days is 0.00005995233 and the variance is 0.516

<h3>The probability that it rains at most 2 days</h3>

The given parameters are:

  • Number of days, n = 7
  • Probability that it rains, p = 95%
  • Number of days it rains, x = 2 (at most)

The probability that it rains at most 2 days is represented as:

P(x ≤ 2) = P(0) + P(1) + P(2)

Each probability is calculated as:

P(x) = ^nC_x * p^x * (1 - p)^{n - x}

So, we have:

P(0) = ^7C_0 * (92\%)^0 * (1 - 92\%)^{7 - 0} = 0.00000002097

P(1) = ^7C_1 * (92\%)^1 * (1 - 92\%)^{7 - 1} = 0.00000168821

P(2) = ^7C_2 * (92\%)^2 * (1 - 92\%)^{7 - 2} = 0.00005824315

So, we have:

P(x ≤ 2) =0.00000002097 + 0.00000168821 + 0.00005824315

P(x ≤ 2) = 0.00005995233

Hence, the probability that it rains at most 2 days is 0.00005995233

<h3>The mean</h3>

This is calculated as:

Mean = np

So, we have:

Mean = 7 * 92%

Evaluate

Mean = 6.44

Hence, the mean is 6.44

<h3>The standard deviation</h3>

This is calculated as:

σ = √np(1 - p)

So, we have:

σ = √7 * 92%(1 - 92%)

Evaluate

σ = 0.718

Hence, the standard deviation is 0.718

<h3>The variance</h3>

We have:

σ = 0.718

Square both sides

σ² = 0.718²

Evaluate

σ² = 0.516

This represents the variance

Hence, the variance is 0.516

Read more about normal distribution at:

brainly.com/question/4079902

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7 0
2 years ago
Shari buys a house for $240,000. She makes a down payment of 20% and finances the rest with a 15 year mortgage. She agrees to ma
Vedmedyk [2.9K]

Answer:

$1166.08 is the monthly payment for the mortgage per month.

Step-by-step explanation:

The meaning of this stated formula on the statement is the present annuity formula because we will have future monthly payments on the mortgage of the house in which they pay off the present value of the house which is $240000 x 80% = $ 192000 as this amount will excludes the down payment of 20% that is made.

We are given Pv the present value which excludes the down payment  $192000.

We have the interest rate i which is 1.2%/12 as it is compounded monthly.

n is the number of payments made over a period which is 12 x 15 years= 180 payments as it is compounded monthly.

no we substitute the above mentioned information to the present value annuity formula stated to calculate R the monthly payment:

Pv = R[(1-(1+i)^-n)/i]

$192000 = R[(1-(1+(1.2%/12))^-180)/ (1.2%/12)] divide both sides by the coefficient of R

$192000/[(1-(1+(1.2%/12))^-180)/(1.2%/12)] = R

$1166.08 =R which this is the amount that will be paid for the mortgage every month for 15 years.

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3 years ago
(3+7i)+(-5+2i)-(-7+6i)
anzhelika [568]
I believe that the answer to your question is 5 + 3 i?
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3 years ago
C
Contact [7]

Answer:

D

Step-by-step explanation:

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What is 7.04 as a fraction and percent
kirill115 [55]
7.04 = 704/100 = 176/25

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