An arts academy requires there to be 4 teachers for every 100 students and 3 tutors for every 30 students. How many students doe
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Set up a system of equations:
x represents how many tee shirts were bought, and y represents how many long sleeve shirts were bought.
For the first equation, subtract y from both sides to get x by itself:
We'll now use substitution. Since x is equal to a value, we can substitute this value for the other equation:
Distribute the 10 to both terms in parentheses:
Combine like terms:
Subtract 90 from both sides:
Divide both sides by -3 to get y by itself:
6 long sleeve shirts were bought.
Now you have a value for y. Input this value into the first equation:
Subtract both sides by 6 to get x by itself:
3 tee shirts were bought.
The answer is B. 3 tee shirts and 6 long sleeve shirts.
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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. =)
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Solve the trigonometric equation:
Restriction for the solution:
Square both sides of (i):
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. =)