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stiv31 [10]
3 years ago
14

Find all solutions of the equation. 5 sin x − 82√ = 3 sin x − 72√

Mathematics
1 answer:
Andrei [34K]3 years ago
6 0

Answer:

  • x = arcsin(√20.5 -3√2) +2kπ . . . k any integer
  • x = π - arcsin(√20.5 -3√2) +2kπ . . . k any integer

Step-by-step explanation:

Add √(82) -3sin(x) to both sides to get ...

  2sin(x) = √82 -√72

Now, divide by 2 and find the arcsine:

  sin(x) = (√82 -√72)/2

  x = arcsin((√82 -√72)/2)

Of course, the supplement of this angle is also a solution, along with all the aliases of these angles.

___

In degrees, the solutions are approximately 16.562° and 163.438° and integer multiples of 360° added to these.

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The answer to the question

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The state of Colorado covers about 1.04 * 105 square miles. The Indian Ocean covers about 2.808 * 107 square miles. How many tim
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Answer:

270 times

Step-by-step explanation:

The number of times Indian Ocean is bigger than Colorado = 28,080,000 ÷ 104,000 = 270 times.

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3 years ago
SOMEONE PLEASE HELP! A survey of a group of seventh graders and a group of teachers at a local middle school asked how many sibl
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<em>Note: You may have missed to add the dot plots chart, so I found the chart after a little research and hence, I am attaching it and based on that dot plot chart I am solving the question which anyways would clear you concept.</em>

Answer:

''The median for the students is 2 and the median for the teachers is 3'' is the right option which compares the medians of the data.

Step-by-step explanation:

Data for students from the dot plot in order

0,\:0,\:1,\:1,\:1,\:1,\:2,\:2,\:2,\:2,\:2,\:2,\:2,\:3,\:3,\:3,\:3,\:3,\:4,\:4

Calculating Median for students:

0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4

As you can see, we do not have just one middle number but we have a pair of middle numbers i.e. 2 and 2, so the median is the average of these two numbers:

Median = (2+2)/2

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            = 2

Data for teachers from the dot plot in order

0, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 8

Calculating Median for teachers:

0, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 8

As you can see, we do not have just one middle number but we have a pair of middle numbers i.e. 3 and 3, so the median is the average of these two numbers:

Median = (3+3)/2

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Therefore, ''the median for the students is 2 and the median for the teachers is 3'' is the right option which compares the medians of the data.

8 0
2 years ago
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Step-by-step explanation:

3 0
3 years ago
Let f(x)=100−10+e−0.1x .
lianna [129]
What are you solving for?
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Let's solve for x.

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Step 2: Factor out variable x.

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Step 3: Divide both sides by f+0.1.

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Answer:

x= e+90/ f+0.1
4 0
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