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lakkis [162]
3 years ago
5

If a and b are two angles in standard position in Quadrant I, find cos(a-b) for the given function values. sin a=3/5and cos b=12

/37
1) 153/185

2) 57/185

3) -57/185

4) -153/185

(Use the sum of identity for cosine)
Mathematics
1 answer:
goldfiish [28.3K]3 years ago
7 0

The identity in question is

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

so that

cos(a - b) = 12/37 cos(a) + 3/5 sin(b)

Since both a and b lie in the first quadrant, both cos(a) and sin(b) will be positive. Then it follows from the Pythagorean identity,

cos²(x) + sin²(x) = 1,

that

cos(a) = √(1 - sin²(a)) = 4/5

and

sin(b) = √(1 - cos²(b)) = 35/37

So,

cos(a - b) = 12/37 • 4/5 + 3/5 • 35/37 = 153/185

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Natalie earned $200 in interest and 30 months with a beginning balance of $1040. What was her interest rate?
rjkz [21]

The interest rate is 7.69%

Step-by-step explanation:

Given

Interest = $200

Time = t = 30 months

Time will be converted into years as the rate is applied yearly

So,

1 year = 12 months

30 months = 30/12 years = 2.5 years

Principal amount  = $1040

The formula for interest is:

I  = P*r*t

Putting the values

200 = 1040 * r * 2.5\\200 = 2600r\\r = \frac{200}{2600}\\r = 0.076923

Converting into percentage:

r = 7.6923

Rounding off to nearest hundredth

r = 7.69%

Hence,

The interest rate is 7.69%

Keywords: Interest, percentage

Learn more about interest at:

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3 years ago
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Ulleksa [173]
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An airplane is loaded with cargo and ready to take off. Before it departs, an unknown number of 8 pound boxes, b, will be taken
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Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

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mestny [16]

Answer:

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Step-by-step explanation:

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V=13,500=b^2*h

The total area of material used is:

A=b^2+4*(b*h)

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