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Colin B.
Tutor for Mathematics, English and Sciences
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Trigonometry
TutorMe
Question:

Solve sin(x)+√(2)=-sin(x) in generality

Colin B.

In this case, we first need to combine terms together by moving the -sin(x) to the left side of the equation. We can do this by adding sin(x) to both sides. This now gives us: 2sin(x)+√(2)=0 From there, we can move the √(2) to the right side of the equation, by subtracting it from both sides. We now have 2sin(x)=-√(2) From here, we can divide both sides by 2, in order to isolate our sin terms. This leaves us with: sin(x)=-√(2)/2 Because sin has a period of 2π, we can determine that the points where the sin(x)=-√(2)/2 are where x=5π/4 and x=7π/4. This would be a stopping point, however, we are looking for all of the possible solutions, which means we need to add in the period of sin(x), for a number of integers that we don't know. For this, we will allow n to represent an integer. Since we know the period is 2π, we will adjust our x values to be: x=5π/4+2nπ and x=7π/4+2nπ

Basic Math
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Question:

Johnny has 12 apples and trades 7 of them away to Susan for all of her 14 oranges. Susan trades those 6 apples away for 3 Snickers bars and a Hershey's Kiss. How many apples and oranges do Johnny and Susan have combined?

Colin B.

Johnny starts with 12 apples and trades 7 away, so he now has 5 apples. In return, he got 14 oranges from Susan. Susan now has 7 apples, but gives 6 away, leaving her with one apple. She did not receive any apples or oranges for this trade. This means, that between the two of them we have Johnny's apples + Susan's apples and Johnny's oranges. Johnny's apples = 5, Susan's apples = 1 and Johnny's oranges = 14. Total apples = 6, Total oranges = 14

Algebra
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Question:

Given the equation 3x^2+14x+7=0, what are the coordinates for the X-Intercepts?

Colin B.

You have 2 main options for solving a quadratic equation. In many cases, you are able to factor the equation to a simplified version. In this case, however, it is not possible to factor the equation at all. The easiest method will then be to use the quadratic formula. The formula is as follows: -b±√ (b^2-4ac) x=_____________ 2a To solve it, we must plug in the a, b, and c coefficients from our given equation. In our case, they are: a=3, b=14 and c=7 When we plug them in we get: -14±√ (14^2-4*3*7) x=_____________ 2*3 Simplified, we get that the above equation is: -14±√ (196-84) x=_____________ 6 -14 ± √ (112) x=___________ 6 -14 ± 4√ (7) x=___________ 6 Solving this, we end up with 2 answers for the x-intercepts: x≈ -0.57 and x≈ -4.1

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