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# Tutor profile: Hyunjune G.

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Hyunjune G.
Volunteered to tutor high school students in mathematics
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## Questions

### Subject:Calculus

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Question:

Integrate the following function from x = pi/2 to x = pi: f(x) = 10sin^4(x)cos(x).

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Hyunjune G.

U-substitution is a way to tackle this problem. We see sin(x) with 4th power. We will choose that as our u. then our du becomes cos(x). Then we integrate: 10u^4du. The result becomes 2sin^5(x) from x = pi/2 to pi. Now, plug in for x: 2sin^5(pi) - 2sin^5(pi/2). Recall that sin(pi) is 0 and sin(pi/2) is 1. Thus, the answer of this integration by u-sub is -2.

### Subject:Algebra

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Question:

Find solutions: y = 3x^3+5x^2-28x

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Hyunjune G.

Finding solutions means finding zeroes. In other words, what would x be when y equals zero? When y = 0, the equation becomes, 0 = 3x^3+5x^2+28x. We see that we can take out x to make the equation like this: 0 = x(3x^2+5x-28). Then, we see whether we can factor out the equation inside the parenthesis. It becomes 0 = x(3x-7)(x+4). Now, let's see which values of x can make the equation 0. Recall 0 times 0 is 0. Therefore, the solutions or the zeroes are x = 0, 7/3, and -4

### Subject:Algebra

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Question:

On one side of a straight road that is 500m long, a planting community decides to plan trees. Each tree takes up 2m of the side of the road. How many trees can the planting community plant on the road?

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Hyunjune G.

The community can plant total of 250 trees on the road. Given that the road is 500m long, let x be the number of trees that the community can plant, and the question says every tree takes up 2m of the the road. That means, every time the community plants a tree, 2m of the distance of the road is covered. Then, you can come up with an equation 2x = 500 (notice the units are the same). Therefore, by dividing 500 by 2, the answer becomes 250 trees that the community can plant.

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