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d1i1m1o1n [39]
3 years ago
10

Find the exact value of the trigonometric expression given that sin u = − 8 17 and cos v = − 24 25 . (Both u and v are in Quadra

nt III.) csc(u − v)
Mathematics
1 answer:
Rashid [163]3 years ago
3 0

Answer: sin u = -5/13 and cos v = -15/17

Step-by-step explanation:

The nice thing about trig, a little information goes a long way. That’s because there is a lot of geometry and structure in the subject. If I have sin u = opp/hyp, then I know opp is the opposite side from u, and the hypotenuse is hyp, and the adjacent side must fit the Pythagorean equation opp^2 + adj^2 = hyp^2.

So for u: (-5)^2 + adj^2 = 13^2, so with what you gave us (Quad 3),

==> adj of u = -12 therefore cos u = -12/13

Same argument for v: adj = -15,

opp^2 + (-15)^2 = 17^2 ==> opp = -8 therefore sin v = -8/17

The cosine rule for cos (u + v) = (cos u)(cos v) - (sin u)(sin v) and now we substitute: cos (u + v) = (-12/13)(-15/17) - (-5/13)(-8/17)

I am too lazy to do the remaining arithmetic, but I think we have created a way to approach all of the similar problems.

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N + 5 ≥ 25
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Of 56 tuna sandwiches sold, 18 were sold on Friday
LuckyWell [14K]

Answer: 32.14   after round off it will be 32

Step-by-step explanation:

This is how to round 32.14 to the nearest whole number. In other words, this is how to round 32.14 to the nearest integer.

32.14 has two parts. The integer part to the left of the decimal point and the fractional part to the right of the decimal point:

Integer Part: 32

Fractional Part: 14

 

Our goal is to round it so we only have an integer part using the following rules:

If the first digit in the fractional part of 32.14 is less than 5 then we simply remove the fractional part to get the answer.

If the first digit in the fractional part of 32.14 is 5 or above, then we add 1 to the integer part and remove the fractional part to get the answer.

The first digit in the fractional part is 1 and 1 is less than 5. Therefore, we simply remove the fractional part to get 32.14 rounded to the nearest whole number as:

32

6 0
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Please help me with this statistics question!!
Dmitry_Shevchenko [17]

a statistic question is with multiple answers

4 0
3 years ago
A marketing firm is considering making up to three new hires. Given its specific needs, the management feels that there is a 50%
IRISSAK [1]

Answer:

a) 0.9

b) Mean = 1.58

Standard Deviation = 0.89

Step-by-step explanation:

We are given the following in the question:

A marketing firm is considering making up to three new hires.

Let X be the variable describing the number of hiring in the company.

Thus, x can take values 0,1 ,2 and 3.

P(x\geq 2) = 50\%= 0.5\\P(x = 0) = 10\% = 0.1\\P(x = 3) = 18\% = 0.18

a) P(firm will make at least one hire)

P(x\geq 2) = P(x=2) + P(x=3)\\0.5 = P(x=2) + 0.18\\ P(x=2) = 0.32

Also,

P(x= 0) +P(x= 1) + P(x= 2) + P(x= 3) = 1\\ 0.1 + P(x= 1) + 0.32 + 0.18 = 1\\ P(x= 1) = 1- (0.1+0.32+0.18) = 0.4

\text{P(firm will make at least one hire)}\\= P(x\geq 1)\\=P(x=1) + P(x=2) + P(x=3)\\ = 0.4 + 0.32 + 0.18 = 0.9

b) expected value and the standard deviation of the number of hires.

E(X) = \displaystyle\sum x_iP(x_i)\\=0(0.1) + 1(0.4) + 2(0.32)+3(0.18) = 1.58

E(x^2) = \displaystyle\sum x_i^2P(x_i)\\=0(0.1) + 1(0.4) + 4(0.32) +9(0.18) = 3.3\\V(x) = E(x^2)-[E(x)]^2 = 3.3-(1.58)^2 = 0.80\\\text{Standard Deviation} = \sqrt{V(x)} = \sqrt{0.8036} = 0.89

7 0
3 years ago
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