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aliya0001 [1]
3 years ago
11

Verify the identity. Show your work. cos(α - β) - cos(α + β) = 2 sin α sin β

Mathematics
1 answer:
s2008m [1.1K]3 years ago
7 0
\bf \textit{Sum and Difference Identities}
\\\\
cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta)
\\\\
cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta)\\\\
-------------------------------

\bf {cos(\alpha - \beta)-cos(\alpha+\beta)}=2sin(\alpha)sin(\beta)
\\\\\\
\stackrel{\textit{left-hand-side}}{[cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta)]-[cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta)]}
\\\\\\
\underline{cos(\alpha)cos(\beta)} + sin(\alpha)sin(\beta)-\underline{cos(\alpha)cos(\beta)} + sin(\alpha)sin(\beta)
\\\\\\
sin(\alpha)sin(\beta)+ sin(\alpha)sin(\beta)\implies 2 sin(\alpha)sin(\beta)
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Alice’s backyard is a rectangular piece of property that is twice as long as it is wide. The total area of her yard is 1,000 m2.
irina [24]
The approximate width of Alice's backyard is 22.36 in.

Let l be the length of the rectangle and w be the width.
l = 2w
A = 1000 m2 = l*w
1000 m2 = 2w *w
500 m2 = w^2
√500 m2 = √w^2
w = <span>22.360679775 in or 22.36 in</span>

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8 0
4 years ago
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The manufacturers of a dietary supplement claim that their product will help customers lose weight. To test their claim, they se
Zielflug [23.3K]

Answer:

Assuming that this data is used to conduct a hypothesis test to test the manufacturers' claim, the test statistic we an use is:

the paired sample t-test.

Step-by-step explanation:

a) Data and Analysis:

Subject   Before   After

1                 225      215

2                245     240

3                 188      188

4                210       212

5               282       175

6               275      260

7               230      225

8               195      200

9               190       185

b) The paired sample t-test is used to compare the means from the same dataset but at different times (say, one month apart).  It supports the comparison of sample data before and after the data subjects have taken the dietary supplement.  When the t-value is high, it is an evidence that the null hypothesis should be rejected.  The higher value of the t-test, therefore, indicates that there is a large difference between the two sample sets.  On the other hand, a small t-value shows similarity between the two sample sets.

3 0
3 years ago
3.152 repeating into a improper fraction
LenaWriter [7]

3  19/125

You can take any number, such as 3.152, and write a 1 as the denominator to make it a fraction and keep the same value, like this:

3.152 / 1

To get rid of the decimal point in the numerator, we count the numbers after the decimal in 3.152, and multiply the numerator and denominator by 10 if it is 1 number, 100 if it is 2 numbers, 1000 if it is 3 numbers, and so on.

Therefore, in this case we multiply the numerator and denominator by 1000 to get the following fraction:

3152 / 1000

Then, we need to divide the numerator and denominator by the greatest common divisor (GCD) to simplify the fraction.

The GCD of 3152 and 1000 is 8. When we divide the numerator and denominator by 8, we get the following:

394 / 125

Therefore, 3.152 as a fraction is as follows:

394 / 125

7 0
3 years ago
Shivani played a video game with three levels. It took her 30 minutes to beat the first level and 1 hour and 45 minutes to beat
Georgia [21]

Answer:

9:30 am

Step-by-step explanation:

  1. Add 30 minutes + 30 minutes to get 60 minutes, which is one hour.
  2. Add 1 hour to 1 hour and 45 minutes to get 2 hours and 45 minutes.
  3. Subtract 2 hours from 12:15 pm, to get 10:15.
  4. That'll leave you with just 45 minutes left. To make it easier than subtract 45 minutes from 10:15, subtract 15 minutes from 10:15, to end up at 10:00 am.
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3 years ago
Please help guys! Using the function f(x) = 3x – 5, what would the output be for an input of 4?
Lelechka [254]

Answer:

Output = 7

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Input value...is the value of x and the output value..is the value of y,

So the question is just saying that what is the value of y when x = 4

; 3(4) - 5

; 12 - 5

; y = 7...therefore the output value = 7

4 0
3 years ago
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