Answer:
a) cos(α+β) ≈ 0.8784
b) sin(β -α) ≈ -0.2724
Step-by-step explanation:
There are a couple of ways to go at these. One is to use the sum and difference formulas for the cosine and sine functions. To do that, you need to find the sine for the angle whose cosine is given, and vice versa.
Another approach is to use the inverse trig functions to find the angles α and β, then combine those angles and find find the desired function of the combination.
For the first problem, we'll do it the first way:
sin(α) = √(1 -cos²(α)) = √(1 -.926²) = √0.142524 ≈ 0.377524
cos(β) = √(1 -sin²(β)) = √(1 -.111²) ≈ 0.993820
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a) cos(α+β) = cos(α)cos(β) -sin(α)sin(β)
= 0.926×0.993820 -0.377524×0.111
cos(α+β) ≈ 0.8784
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b) sin(β -α) = sin(arcsin(0.111) -arccos(0.926)) ≈ sin(6.3730° -22.1804°)
= sin(-15.8074°)
sin(β -α) ≈ -0.2724
Answer:
No Solutions
Step-by-step explanation:
We have to create an equation to be able to solve this problem.
Let's let x = the # of home runs
The equation that helps us solve this is 5 + 1x = 10 + 1x
First, we have to subtract 1x from each side (always subtract the variable first before the constant, math rule)
This brings us to 5=10 because the x's cancel each other out.
You probably look at this saying, wait, this isn't right, and you would be correct
Since this equation isn't true, it is No Solutions
No Solutions mean there is no answer to the problem, it is impossible to solve.
So, our final answer is No Solutions
Hope this helps, have a great day! :)
Answer: It is believed that exactly 20% of Evergreen Valley college students attended the opening night midnight showing of the latest harry potter movie.
Step-by-step explanation:
Since we have given that
n = 84
x = 11
So, 
p = 0.20
So, hypothesis:
so, test statistic value would be
At 1% level of significance, critical value would be
z= 2.58
Since 2.58>-1.604
So, We will accept the null hypothesis.
Hence, It is believed that exactly 20% of Evergreen Valley college students attended the opening night midnight showing of the latest harry potter movie.
Answer:
im not sure what you mean can you elaborate
Step-by-step explanation:
Putting this as an arithmetic sequence gives:
The sum of the series = 16 x 7 x 7 = 784 m^3 = 784 000 L
The sum of an arithmetic series can be written as:
![S_n=n/2 [2a+(n-1)d] = 784 000 \\n/2[2(150)+(n-1)200] = 784 000 \\n[300+200(n-1)=1 568 000 \\300n+200n^2-200n = 1 568 000 \\200n^2+100n- 1 568 000 = 0 \\2n^2 +n- 15680 = 0 \\n= 88.2...,-88.7](https://tex.z-dn.net/?f=S_n%3Dn%2F2%20%5B2a%2B%28n-1%29d%5D%20%3D%20784%20000%0A%5C%5Cn%2F2%5B2%28150%29%2B%28n-1%29200%5D%20%3D%20784%20000%0A%5C%5Cn%5B300%2B200%28n-1%29%3D1%20568%20000%0A%5C%5C300n%2B200n%5E2-200n%20%3D%201%20568%20000%0A%5C%5C200n%5E2%2B100n-%201%20568%20000%20%3D%200%0A%5C%5C2n%5E2%20%2Bn-%2015680%20%3D%200%0A%0A%5C%5Cn%3D%2088.2...%2C-88.7)
n has to be positive, so we get
n =
<u>88.2 hours (3 s.f.)</u>
