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3 years ago

If x = a sin teta and y = b cos teta

Mathematics

1 answer:

Marat540 [252]3 years ago

8 0

x= a sin theta
y=b sin theta

$\\ \sf\longmapsto b^2x^2+a^2y^2$

$\\ \sf\longmapsto b^2(asin\Theta)^2+a^2(bcos\Theta)^2$

$\\ \sf\longmapsto b^2a^2sin^2\Theta+a^2b^2cos^2\Theta$

$\\ \sf\longmapsto a^2b^2(sin^2\Theta+cos^2Theta)$

$\\ \sf\longmapsto a^2+b^2(1)$

$\\ \sf\longmapsto a^2b^2$

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Helpp picture about will mark

dezoksy [38]

Answer:

Step-by-step explanation:

3*2=6

6^2 is 36

8 0

3 years ago

I need help on 19 and 20. Please help me. Please don’t put a link. Please help me.

lianna [129]

Answer:

19:

4 < third side < 14

20:

3 < third side < 13

Step-by-step explanation:

hint: go to http://www.17 28.org/trianinq.htm

(fix the space between 17 and 28)

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3 years ago

A shopkeeper bought a pen at rs 20 and sold at rs25 find his profit or loss

Alina [70]

The profit is 5rs because 25-20=5rs

3 0

4 years ago

Rachel has 60 scones. She sells them to Robbie, Cameron, Louis, Tom and Charlie in that order. Each customer buys more scones th

Korvikt [17]

Robbie bought the smallest amount. Let's use x for that amount.
Let's use n for amount that each following customer increases.

We have:
Robbie=x
Cameron=x+n
Louis=x+n+n
Tom=x+n+n+n
Charlie=x+n+n+n+n

We know that they bought total of 60 scones.
Robbie + Cameron + Louis + Tom + Charlie = 60
x + x+n + x+n+n + x+n+n+n + x+n+n+n+n = 60
5x + 10n = 60 /:5
x + 2n = 12

We are also given this information:
(Robbie + Cameron) = 3/7 * (Louis + Tom + Charlie)
We insert the equations from above:
(x + x+n) = 3/7 * (x+n+n + x+n+n+n + x+n+n+n+n)
2x + n = 3/7 * (3x + 9n) /*7
14x + 7n = 3* (3x + 9n)
14x +7n = 9x + 27n
We take everything on the left side.
14x + 7n - 9x - 27n = 0
5x - 20n = 0/:5
x - 4n = 0

Now we have two equations:
x + 2n = 12
x - 4n = 0
We solve second one for x and insert it into first one.
x + 2n = 12
x = 4n

4n + 2n =12
6n = 12 /:6
n = 2
x=4*2
x=8

Now we can solve for the amount for each customer.
Robbie=x = 8
Cameron=x+n = 8 + 2 = 10
Louis=x+n+n = 8 + 2 + 2 = 12
Tom=x+n+n+n = 8 + 2 + 2 + 2 = 14
Charlie=x+n+n+n+n = 8 + 2 + 2 + 2 + 2 = 16

7 0

3 years ago

A car insurance company has high-risk, medium-risk, and low-risk clients, who have, respectively, probabilities .04, .02, and .0

Paha777 [63]

Answer:

(a) 0.983

(b) 0.353 or 35.3%

Step-by-step explanation:

a) The probability of a random client does not file a claim is equal to the sum of:

1) the probability of a client being high risk and does not file a claim = P(hr)*(1-P(c_hr))

2) the probability of a client being medium risk and does not file a claim = P(mr)*(1-P(c_mr))

and

3) the probability of a client being low risk and does not file a claim = P(lr)*(1-P(c_lr))

P(not claim) = P(hr)*(1-P(c_hr))+P(mr)*(1-P(c_mr))+P(lr)*(1-P(c_lr))

P(not claim) = 0.15*(1-0.04)+0.25*(1-0.02)+0.6*(1-0.01)

P(not claim) = 0.15*0.96+0.25*0.98+0.6*0.99 = 0.983

(b) To know the proportion of claims that come from high risk clients we need to know the total expected claims in every category:

Claims expected by high risk clients = P(c_hr)*P(hr) = 0.04*0.15 = 0.006 claims/client

Claims expected by medium risk clients = P(c_mr)*P(mr) = 0.02*0.25 = 0.005 claims/client

Claims expected by low risk clients = P(c_lr)*P(lr) = 0.01*0.60 = 0.006 claims/client

The proportion of claims done by high risk clients is

Claims by HR clients / Total claims expected = 0.006 / (0.006+0.005+0.006) = 0.006 / 0.017 = 0.3529 or 35,3%

1) High risk: 0.15*(1-0.04) = 0.144

2) Medium risk: 0.25*(1-0.02) = 0.245

3) Low risk: 0.6*(1-0.01) = 0.594

The probability that a random client who didn't file a claim is low- risk can be calculated as:

Probability of being low risk and don't file a claim / Probability of not filing a claim

P(LR&not claim)/P(not claim) = 0.594 / (0.144+0.245+0.594)

P(LR&not claim)/P(not claim) = 0.594 / 0.983 = 0.604 or 60.4%

6 0

3 years ago