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Minchanka [31]
2 years ago
15

Find the exact value of the trigonometric function given that sinU=-7/25 and cosV=-4/5 (Both U and V are in Quadrant III)

Mathematics
1 answer:
Contact [7]2 years ago
3 0

cosU:-

\\ \rm\longmapsto \sqrt{1-sin^2U}=\sqrt{1-49/625}=24/25

As U lies in Q3

  • cosU=-24/25

sinV

\\ \rm\longmapsto \sqrt{1-cos^2V}=\sqrt{1-16/25}=3/4

As V lies in Q3

  • sinV=-3/5

So

  • sin(V-U)=sinVcosU-cosVsinU=(-3/5)(-24/25)-(-4/5)(-7/25)=72/125-28/125=72-28/125=<u>4</u><u>4</u><u>/</u><u>1</u><u>2</u><u>5</u>
  • cos(U-V)=cosUcosV+sinUsinV=(-24/25)(-4/5)+(-7/25)(-3/5)=96/125+21/125=117/125
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Mrs. Daly's reading classes were surveyed about their reading preferences. The data is summarized in the table below.
andriy [413]

Answer:

Required probability is 0.19

Step-by-step explanation:

The two-way table for the given data is,

                              Fiction                Non-Fiction                Total

9th grade                35                            8                             43

10th grade               52                            12                           64

Total                        87                            20                           107

It is required to find the probability of the students who prefer to read non-fiction novels, given that they are in 9th grade.

That is, to find the conditional probability P(Non-fiction| 9th\ grade).

Now, P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}

So, we get,

P(Non-fiction| 9th\ grade)=\dfrac{(Non-fiction\bigcap 9th\ grade)}{P(9th\ grade)}\\\\P(Non-fiction| 9th\ grade)=\dfrac{8}{43}\\\\P(Non-fiction| 9th\ grade)=0.19

<h3>Thus, the required probability is 0.19.</h3>
5 0
3 years ago
Explain why their are no solutions to the system of inequalities <br> y ≤2x-5 <br> y ≥2x+1
rosijanka [135]

Answer:

Sorry this is late and I think this is right.

They are both parallel, they have the same slope, and do <em>not </em>intersect. If you were to draw a slope out for it, you would find this to be true.

For example: Say the question called for you to explain why there aren't any solutions to these system of inequalities:

<em>y < - 1/2x -3</em>

<em>y > 1/2x + 2</em>

<em>y= -x/2 -3</em> and <em>y= -x/2 + 2 </em>have the same exact slope, are parallel, and never intersect. The first line is 5 units below the second line when x = 0. Because the lines are parallel, it is always below the second line. The solutions of y < - x/2 -3 are the points in the plane below the first line. The solutions of y > 1/2 + 2 are points above the second line.

I hope this helps you. Good luck on whatever you're working on and stay safe! Please let me know if this helped you or didn't.

7 0
3 years ago
Charlie wants a new pair of shoes that cost $40. His mom pays 75% of the cost and charlie pays 25%. How much do they each pay?
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In order to find out how much they both each pay, you would have to put two places in front of the percentage of the payment.
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3 years ago
Work out the area of this circle. Take pi to be 3.142 and give your answer to 1 decimal place
Rashid [163]

Step-by-step explanation:

<em>I think you have forgotten to attach the question. </em>

<em>Anyways....</em>

In order to find the area of a circle use the formula:

πr^{2}   Where r is the radius

For example the radius is 3cm. The area of the circle will be:

π × 3^{2}

Since you have taken pi as 3.142...

3.142 × 3^{2}

3.142  × 9

= 28.278

In order to find the answer to 1 decimal place, check the number next to the number right after the decimal. Is it a number greater than or equal to 5? then add +1 to the number.

= 28.3 cm^{2}

8 0
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If you use 104 kiloliters of water per year, approximately how many liters of water do you use in a day?
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Answer:

0.28 liters

Step-by-step explanation:

104÷365=0.28

5 0
3 years ago
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