Answer:
Answer is D
Step-by-step explanation:
Answer: 15 + 53/77
Step-by-step explanation:
Multiplying a fraction by 1 does not change the value.
Any number divided by itself is 1.
For instance, 11/11 = 7/7 = 1.
12 + 1/7 + 3 + 6/11 = 15 + 1/7 + 6/11
= 15 + (11×1)/(11×7) + (7×6)/(7×11)
= 15 + 11/77 + (6×7)/77
= 15 + (11 + 6×7)/77
= 15 + 53/77
It is faster to make sure to multiply by the "smallest" form of one that will work, but you don't have to. You only need to make sure that at the end there are no common factors in numerator and denominator, and that numerator is smaller than denominator.
Any number larger than 36 would be a counter examples.
When n is equal to 36, both sides of the inequality are equal to 216. As you get larger than 36 the right side is larger than the left side. Therefore, the inequality is not true.
Answer:
2sin(2x)-2sinx+2sqrt3cosx-sqrt3 = 0
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4sin(x)cos(x) - 2sin(x) + 2sqrt(3)cos(x) - sqrt(3) = 0
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Factor:
2sin(x)[2cos(x)-1] + sqrt(3)[2cos(x)-1] = 0
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[2cos(x)-1][2sin(x)+sqrt(3)] = 0
Solve:
2cos(x)-1 = 0 or 2sin(x)+sqrt(3) = 0
cos(x) = 1/2 or sin(x) = -sqrt(3)/2
x = +/-pi/3 or x = -pi/3 or (4/3)pi
hope this helps!
