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olganol [36]
3 years ago
8

Find the exact value of cos (u-v) given that sin u=-9/41 and cos v=15/17. (Both u and v are in quadrant IV)

Mathematics
1 answer:
siniylev [52]3 years ago
8 0
Please review the sum and difference formulas for the trig functions.

In this case you have the difference between two angles u and v and want to find the cosine of this difference.

Here's the appropriate formula:  

cos (a-b) = cos a cos b + sin a sin b

Given that sin u = -9/41, equal to the opp side over the hyp., we must find the length of the adj. side and then u itself.

opp side = - 9
hyp =           4
adj side = sqrt( 18+4) = sqrt(22)

Find the side opp angle v in a similar manner.

Then cos (u-v) = cos u cos v + sin u sin v becomes

                        = (cos u)(15/17) + (-9/41)(sin v)   (where you must find cos u and sin v)

See what you can do, then return and comment here if you need further help.  Good luck.

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You decide to enter in a rowing competition. To train, you go to the boat house and begin rolling down stream. You row for the s
fredd [130]

Answer:

Time spent rowing down stream =100\ seconds

Speed of boat in still water =14\ ms^{-1}

Step-by-step explanation:

Let speed of boat in still water be = x\ ms^{-1}

Speed of current = 10\ ms^{-1}

Speed of boat down stream = \textrm{Speed of boat in still water +Speed of current}= (x+10)\ ms^{-1}

Distance rowed down stream = 2400 m

Time spent rowing down stream = \frac{Distance}{Speed}=\frac{2400}{x+10}\ s = \frac{Distance}{Speed}=\frac{2400}{x+10}\ s

Speed of boat up stream = \textrm{Speed of boat in still water -Speed of current}= (x-10)\ ms^{-1}

Distance rowed up stream = \frac{1}{6} \textrm{ of distance rowed downstream}=\frac{1}{6}\times 2400 = 400\ m

Time spent rowing up stream = \frac{Distance}{Speed}=\frac{400}{x-10}\ s

We know that,

\textrm{Time spent rowing down stream =Time spent rowing up stream}

So,

\frac{2400}{x+10}=\frac{400}{x-10}

Cross multiplying

2400(x-10)=400(x+10)

Dividing both sides by 400

\frac{2400(x-10)}{400}=\frac{400(x+10)}{400}

6(x-10)=x+10

6x-60=x+10

Adding 60 to both sides.

6x-60+60=x+10+60

6x=x+70

Subtracting both sides by x

6x-x=x+70-x

5x=70

Dividing both sides by 5.

\frac{5x}{5}=\frac{70}{5}

∴ x=14

Speed of boat in still water =14\ ms^-1

Time spent rowing down stream =\frac{2400}{14+10}=\frac{2400}{24}=100\ s

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3 years ago
Question Which sequence of transformations maps pre-image ABC to image A′B′C′ ? Triangle ABC was reflected over the y-axis and t
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The sequence of transformations was Triangle ABC was reflected over the y-axis and then translated 2 units up and 2 units to the right.

<h3>What is a transformation?</h3>

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Rigid transformation is the transformation that does not change the shape or size of a figure. Examples of rigid transformations are <em>translation, reflection and rotation</em>.

Find out more on transformation at: brainly.com/question/4289712

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2 years ago
Identify the interquartile range for the set of values below. 37, 34 , 29 , 33, 35 , 30 , 34 A) 4 B) 5 C) 3 D) 8
dusya [7]

Answer:25th Percentile: 5

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75th Percentile: 34

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Step-by-step explanation:

8 0
3 years ago
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What is arccos(−1) in Radians.
Free_Kalibri [48]

Answer:

π radians

Step-by-step explanation:

The arc cos(- 1) in degrees is 180° and 180° = π radians

7 0
3 years ago
How do you you divide 67by6
Law Incorporation [45]
You first set it up as long division. 
Second you would find out how many times 6 goes into 67, so count by 6's until you get close 67.
Third once you get that number you write it on top of the long division and then you would subtract whatever that number is below which is 66 because 6 * 11= 66.
So then you would subtract 67 minus 66 which would be 1. Then go from there and you'll get your answer.

Hope this helps!
6 0
3 years ago
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