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emmasim [6.3K]
2 years ago
14

4cos^2(x)-7cos(x)+3 Please help and explain how you did it :)

Mathematics
1 answer:
dangina [55]2 years ago
7 0

I assume you're asked to solve

4 cos²(<em>x</em>) - 7 cos(<em>x</em>) + 3 = 0

Factor the left side:

(4 cos(<em>x</em>) - 3) (cos(<em>x</em>) - 1) = 0

Then either

4 cos(<em>x</em>) - 3 = 0   <u>or</u>   cos(<em>x</em>) - 1 = 0

cos(<em>x</em>) = 3/4   <u>or</u>   cos(<em>x</em>) = 1

From the first case, we get

<em>x</em> = cos⁻¹(3/4) + 2<em>nπ</em>  <u>or</u>   <em>x</em> = -cos⁻¹(3/4) + 2<em>nπ</em>

and from the second,

<em>x</em> = <em>nπ</em>

where <em>n</em> is any integer.

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Answer: Choice B) (24,10)

---------------------------------------------------------

Work Shown:

2x - 4y = 8
2( x ) - 4y = 8
2( 3y-6 ) - 4y = 8 ... notice x has been replaced with 3y-6
2(3y)+2(-6) - 4y = 8
6y-12 - 4y = 8
2y-12 = 8
2y-12+12 = 8+12 ... add 12 to both sides
2y = 20
2y/2 = 20/2 ... divide both sides by 2
y = 10

If y = 10, then
x = 3y-6
x = 3*10-6 ... replace y with 10
x = 30-6
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Put together, the solution is (x,y) = (24,10)
which is why the answer is choice B

As a check, we can plug (x,y) = (24,10) into each equation
x = 3y-6
24 = 3*10 - 6
24 = 30 - 6
24 = 24 ... true equation
and similarly for the second equation as well
2x-4y = 8
2*24 - 4*10 = 8
48 - 40 = 8
8 = 8 ... true equation
Both equations are true when (x,y) = (24,10) so the solution is confirmed
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Answer:

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