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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
Find out the ratio of price to pound for each bag.
To prove
As given
A store sells grass seed in small bags and large bags.the small bags have 7 pounds of seed for $27.93 .
7 pound = $27.93
Now find out the cost for the 1 pound.
1 pound cost = $3.99
As given large bags cost $66.98.
Now find out pounds in the large bags.
Let us assume that the number of pounds in the large bags be x.
Than
3.99 × x = 66.98
x = 16.8 pounds (approx)
Now find out the ratio of price to pound for each bag.
As small bags weight = 7 pounds
Cost of the small bags = $27.93
As large bags weight = 16.8 pounds
Cost of the large bags = $66.98
Hence proved
Answer:
a.) First check on the height of the bar that ranges between 20 and 24 which is 6. The 6 is the number of students who bought 20 books or more, so get the percentage of those students who bought 20 or more books; divide 6 which is the number of students who bought 20 books or more with the total number of students which is 40 then multiply with 100.
% of students who bought 20 or more books = 6/40 ×100
=15
Step-by-step explanation:
b.) Find the area of a trapezium
= 1/2 × {a+b} × h
= 1/2 × {9 + 13} ×12
= 132
= 1/2 × {13 + 6} × 12
= 108
Mean no. of books bought = 132 + 108
= 240
Easy divide the $ by the yards then multiply the number of $ to the amount needed ;D
