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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. =)
Answer:
4
Step-by-step explanation:
- If you take the lowest half of the data (from the lower extreme to the median) and find the median of these numbers, that is called the lower quartile or quartile 1.
- If you take the upper half of the data (from the upper extreme to the median) and find the median of these numbers, that is called the upper quartile or quartile 3.
- The interquartile range is the difference between quartile 1 and quartile 3.
- 4, 5, 6, 8, 9, 10, 11, 13
- Median=8.5
- Q1=6.5
- Q3=10.5
- 10.5-6.5=4
I also added my PowerPoint if you didn't get what I was saying.
Answer:
Two parallel lines
Step-by-step explanation:
the slopes are the same: slope = 3
f(x) 3x + 5 g(x) = 3x - 2
Pick at least three x values and find their corresponding values for y. Remember the f(x) and g(x) represent y
f(x) = 3x + 5 g(x) = 3x - 2
y = 3x + 5 y = 3x - 2
let x = 0 y = 3(0) + 5 y = 3(0) - 2
y = 5 y = -2
Ordered pair (0, 5) (0, -2)
Let x = 1 y = 3(1) +5 y = 3(1) - 2
y = 8 y = 1
ordered pair (1, 8) (1, 1)
Let x = -1 y = 3(-1) + 5 y = 3(-1) - 2
y = 2 y = -5
ordered pair (-1, 2) ( -1, -5)
Locate the ordered pairs and draw the graph on the lines.
you will graph two parallel lines
Answer:
5.2%po joke Lang Hahahahahahah
Answer:
332
Step-by-step explanation:
To find how many seats there were, multiply the number of rows with the number of seats in each row:
15 (24) = 360
From these total seats, there are 28 empty seats, meaning:
360 - 28 = 332
There were 332 people.
