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3 years ago

Find the exact value of tan(x-y) if sinx=8/17 and cosy=3/5

2 answers:

8 0

To solve the the question we proceed as follows:
From trigonometric laws
(cos x)^2+(sin x)^2=1
(cos y)^2+(sin y)^2=1
sin (x-y)=sin x sin y-sin y cos x
cos (x-y)=cos x cos y+ sin x sin y
si x=8/17
cos x=sqrt(1-(sin x)^2)=sqrt(1-64/289)=sqrt(225/289)=15/17
cos y=3/5
sin x= sqrt(1- (cos x)^2)= sqrt(1-9/25)=sqrt(16/25)=4/5
thus
tan (x-y)=[sin (x-y)]/[cos (x-y)]
=[sin x cos y-sin y cos x]/[cos x cos y+sin x sin y]
plugging in the values we obtain:
[8/17 *3/5-4/5*15/7]/[15/17*3/5+8/17*4/5]
simplifying
[24/85-60/85]/[45/85+32/85]
=-36/77

makkiz [27]3 years ago

6 0

Answer:

Step-by-step explanation:

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aleksandr82 [10.1K]

Answer:D

Step-by-step explanation: It is none of them because it is translated up one unit and then reflected across the y axis.

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2 years ago

Use a net to find the surface area of the cone to the nearest square centimeter. Use 3.14 for pi (Round to nearest whole number)

Mariana [72]

Given:

The radius of the base of the given cone = 5 cm

The slant height of the cone = 19 cm

To find the surface area of the given cone.

Formula

The surface area pf the given cone is,

where, r be the radius and

l be the slant height.

Now,

Taking, r = 5, l = 19 and π = 3.14 we get,

sq cm

or, sq cm

Rounding off to the nearest square centimeter, we get;

Hence,

The surface area of the cone is 377 sq cm.

3 0

3 years ago

There is a bag of 50 marbles.

SVETLANKA909090 [29]

Answer:

If you want to find the probability of picking out a certain colored marble after you have already picked one out, then the probability changes, because now the total number of marbles you have is 32 instead of 33, and the probability of the color you could pick out can change depending on what marble you picked out first.

For example, if you want to know the probability of picking out an orange marble the second time, and you didn't pick out a orange marble the first time, then you still have 10 orange marbles, but now you have 32 total marbles, so the probability will be 10 out of 32 instead of 10 out of 33. But if you picked out 1 orange marble already, and you didn't put it back in, then you will have a probability of picking out 9 out of 32 because there are 9 orange marbles left.

In short: If you pick a marble out the first time and then put it back in the pile before your friend picks one out, then the probability of picking a marble of a certain color will be the same the second time as the first time because there will still be the same number of marbles with the same number of the same colored marbles as the first time, but if you don't put the marble back in, then the probabilities will change.

Step-by-step explanation:

7 0

3 years ago

Is (5,-2) a solution of the graphed inequality?

amid [387]

Answer: yes

Step-by-step explanation:

Yes, because it is in the shaded part. Anything in the line or shaded part are part of the answer :)

3 0

3 years ago

180kg, 250kg, 200kg, 209kg, 195kg, 205kg, 190kg, 188kg, 192kg. What is the IQR of the lion's weights.

velikii [3]

Answer:

Step-by-step explanation:

Given the data:

180kg, 250kg, 200kg, 209kg, 195kg, 205kg, 190kg, 188kg, 192kg

The interquartile range (IQR) = Q3 - Q1

Reordering the data:

180, 188, 190, 192, 195, 200, 205, 209, 250

Q3 = 3/4(n+1)th term

Q3 = 3/4(10) = 7.5 th term = (205+209)/2 = 207

Q1 = 1/4(n+1)th term

Q1 = 1/4(10) = 2.5th term = (188+190)/2 = 189

Q3 - Q1 = 207 - 189 = 18

3 0

3 years ago