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jeyben [28]
3 years ago
10

What values for theta (0 less than or equal to theta less than equal to 2pi) satisfy the equation?

Mathematics
1 answer:
Novosadov [1.4K]3 years ago
7 0
Solve this as you would an equation that does not involve trig.  Don't let the trig scare you.  If you had to solve 2x+8=0, the first thing you would do is factor out the common 2.  In our equation, we have a common cos theta.  I'm going to use beta as my angle.  When we factor out beta, here's what we have. cos \beta (2sin \beta +1)=0.  The Zero Product Property tells us that at least one of those factors has to equal zero.  So we set them both equal to zero and solve.  Let's get the equations first, then we will need our unit circle.  First equation set to equal zero is cos \beta =0.  On our unit circle, cos is the value inside the parenthesis that is in the x position within our coordinate.  Look at all those coordinates as you go around the unit circle once (once around is equivalent to 2pi).  You will find that the the cos is 0 at \frac{ \pi }{2}, \frac{3 \pi }{2}.  The next equation is 2sin\beta +1=0.  Move the 1 over by subtraction and divide by 2 to get sin \beta =- \frac{1}{2}.  Same as before, go around the unit circle one time and look to see where the coordinate in the y place is -1/2.  Sin corresponds to the y coordinate.  You will find that sin is -1/2 at \frac{7 \pi }{6}, \frac{11 \pi }{6}.  And there you go!  Trig is so much fun!!!
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A research study investigated differences between male and female students. Based on the study results, we can assume the popula
garri49 [273]

Using the <u>normal distribution and the central limit theorem</u>, it is found that the interval that contains 99.44% of the sample means for male students is (3.4, 3.6).

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • It measures how many standard deviations the measure is from the mean.  
  • After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation s = \frac{\sigma}{\sqrt{n}}.

In this problem:

  • The mean is of \mu = 3.5.
  • The standard deviation is of \sigma = 0.5.
  • Sample of 100, hence n = 100, s = \frac{0.5}{\sqrt{100}} = 0.05

The interval that contains 95.44% of the sample means for male students is <u>between Z = -2 and Z = 2</u>, as the subtraction of their p-values is 0.9544, hence:

Z = -2:

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

-2 = \frac{X - 3.5}{0.05}

X - 3.5 = -0.1

X = 3.4

Z = 2:

Z = \frac{X - \mu}{s}

2 = \frac{X - 3.5}{0.05}

X - 3.5 = 0.1

X = 3.6

The interval that contains 99.44% of the sample means for male students is (3.4, 3.6).

You can learn more about the <u>normal distribution and the central limit theorem</u> at brainly.com/question/24663213

7 0
2 years ago
X:y=5:3 and x+y=56 work out the value of x-y
Vladimir79 [104]

x - y = 14

given the ratio x : y = 5 : 3

then let x = 5x and y = 3x, hence equation can be expressed as

5x + 3x = 56

8x = 56 ( divide both sides by 8 )

x = 7

Hence x = 5 × 7 = 35 and y = 3 × 7 = 21

Thus x - y = 35 - 21 = 14


6 0
3 years ago
Evaluate: 45 n=1(4n +9) = [?]
Alenkasestr [34]

Answer: 4545

Step-by-step explanation:

Split the summation into smaller summations that fit the summation rules.

7 0
3 years ago
Make a proof ( Statements and reasons )
frosja888 [35]

Step-by-step explanation:

They are equal because when we flip or reflect ABC onto DCB we are going to have the same size and the same shape

4 0
3 years ago
Express simplest form
Genrish500 [490]

p\%=\dfrac{p}{100}\\\\2\dfrac{1}{2}\%

<em>Convert the mixed number to the improper fraction.</em>

2\dfrac{1}{2}=\dfrac{2\cdot2+1}{2}=\dfrac{5}{2}


2\dfrac{1}{2}\%=\dfrac{5}{2}\%=\dfrac{\frac{5}{2}}{100}=\dfrac{5}{2}\cdot\dfrac{1}{100}=\dfrac{1}{2}\cdot\dfrac{1}{20}=\dfrac{1}{40}

7 0
3 years ago
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