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Solve the trigonometric equation:
Restriction for the solution:
Square both sides of
(i):
![\mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left[2\cdot (1-sin^2\,x)-sin\,x \right]=0}\\\\\\ \mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left[2-2\,sin^2\,x-sin\,x \right]=0}\\\\\\ \mathsf{-\,\dfrac{sin\,x}{cos^2\,x}\cdot \left[2\,sin^2\,x+sin\,x-2 \right]=0}\\\\\\ \mathsf{sin\,x\cdot \left[2\,sin^2\,x+sin\,x-2 \right]=0}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cdfrac%7Bsin%5C%2Cx%7D%7Bcos%5E2%5C%2Cx%7D%5Ccdot%20%5Cleft%5B2%5Ccdot%20%281-sin%5E2%5C%2Cx%29-sin%5C%2Cx%20%5Cright%5D%3D0%7D%5C%5C%5C%5C%5C%5C%20%5Cmathsf%7B%5Cdfrac%7Bsin%5C%2Cx%7D%7Bcos%5E2%5C%2Cx%7D%5Ccdot%20%5Cleft%5B2-2%5C%2Csin%5E2%5C%2Cx-sin%5C%2Cx%20%5Cright%5D%3D0%7D%5C%5C%5C%5C%5C%5C%20%5Cmathsf%7B-%5C%2C%5Cdfrac%7Bsin%5C%2Cx%7D%7Bcos%5E2%5C%2Cx%7D%5Ccdot%20%5Cleft%5B2%5C%2Csin%5E2%5C%2Cx%2Bsin%5C%2Cx-2%20%5Cright%5D%3D0%7D%5C%5C%5C%5C%5C%5C%20%5Cmathsf%7Bsin%5C%2Cx%5Ccdot%20%5Cleft%5B2%5C%2Csin%5E2%5C%2Cx%2Bsin%5C%2Cx-2%20%5Cright%5D%3D0%7D)
Let
So the equation becomes
Solving the quadratic equation:
You can discard the negative value for
t. So the solution for
(ii) is
Substitute back for
t = sin x. Remember the restriction for
x:
where
k is an integer.
I hope this helps. =)
24)y=x-4
21) y=-3x+1
23) y=4/5x+6
Hello! I would love to help!
9. Basically, it is asking us to multiply 5.2 by 46.
5.2*46=239.2
So, your answer is 239.2 inches.
10. First, let's find out how many blocks she has left to run by subtracting the number of blocks she has already ran by the number of total blocks.
60-18=42
So Susan has 42 blocks left to run. Now, let's divide that by 2 since she can run 2 blocks per minute.
42/2=21
So, the answer is 21 minutes.
11. Let's set up an equation: We know that she will automatically pay $49.95 per month, plus $0.15 per additional minute. We also know her final total for the month was $61.20:
49.95+0.15m=61.20
Let's solve! Subtract both sides by 49.95
49.95+0.15m-49.95=61.20-49.95
Simplify
0.15m=11.25
Now, divide both sides by 0.15
0.15m/0.15=11.25/0.15
M=75
So your answer is 75 additional minutes.
Hope this helped! Comment if you have questions!
Answer:
12 liters
Step-by-step explanation:
Let the capacity sum of the 5 containers be X
13 = X / 5
X = 65 liters
Average capacity of the six = ( 65 + 7 )/ 6 liters
= 72/6 liters
= 12 liters
Answer:
-8, 0
Step-by-step explanation:
The floor and ceiling functions have equal values for any integer argument. Their value is that integer.
Among your answer choices, the integers are -8 and 0.
