Cole H.

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Pre-Calculus

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Question:

Solve for x: ln(4x)-ln(2)=1

Cole H.

Answer:

log rules log(a)-log(b)=log(a/b) ln(4x/2)=1 drop base e to both sides 4x/2=e x=e/2

Trigonometry

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Question:

Given a right triangle with a side length of 4 and the opposite angle being 45 degrees what is the length of the other two sides?

Cole H.

Answer:

I chose this question because a 45-45-90 question because most can guess the solution but now you get to see the process of finding it so they get the satisfaction of knowing they found the right answer. So using SOH-CAH-TOA and that we have the angle and the known sidelength opposite of eachother we are going to want to use sin or tangent. We will use tan to work this one out however both ways are possible: tan(x)=O/A, tan(45)=4/A, A=4/tan(45), A=4, as you would have probably guessed. From here we can use Pythagorean theorem or now that we have both sides you may use sin or cos.

Algebra

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Question:

Find the roots of the following equation using the quadratic equation: y=x^2+6x+8

Cole H.

Answer:

As found in text books and you may want to put to memory the quadratic formula. A= the coefficient of our x^2 term so in this case it equals 1 B= the coefficient of our x term which is 6 and C= the constant, 8 Using these in the formula (-b+/-sqrt(b^2-4ac))/2a) After plugging the correct values in you will get two answers(one from each +/- in the equation) you will get the answers of -2,-4. Which we can check through factoring if we'd like: (x+4)(x+2)=y y=0 when x=-2,-4 so our answer is correct!

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