# Tutor profile: Lea H.

## Questions

### Subject: Pre-Calculus

Solve the equation: x = 4(cube root x)

First, I will demonstrate how cubing a cube root or squaring a square root results in them canceling each other out. But, to do this, you need to cube the entire expression. So cubing the entire expression will result in: x cubed = 64x We have 64 because 4x4x4 = 64. The next step is having the equation equal zero, so subtract 64x from both sides: x cubed - 64x = 0 Next, we should recognize that 64 is a perfect square, meaning its square root is a perfect integer, 8. Once we know that squaring 64 gives us 8, we should make sure that everything else can be squared as well because we can't apply one function to one part of the expression; it needs to be applied to the whole expression. BUT, there's nothing else that can be squared, because the x is cubed. So we need to create the square root by factoring out ONE of the THREE x's. So: x(x squared - 64) = 0 NOW, we can find the square root of (x squared - 64), which is: (x-8)(x+8) The reason why we have a positive and negative 8 is because if we just had them positive, we would have 64, because 8x8=64, but in the previous step we found that it was (x squared MINUS 64), so that means two things multiplied resulted in a negative 64. They can't both be negative, because negative multiplied by negative results in a positive number. Hence, we have one positive and one negative. So what we have now is: 0 = x(x-8)(x+8) Finally, we can see that our answer is: x = 0, 8, or -8, because if we input all of those for x, we will end up with 0 = 0 We should prove that by inputting each of them to double check that we are correct.

### Subject: Biology

What is the difference between plant and animal cells?

First, I will outline what they have in common: cell membrane, nucleus, mitochondria, and vacuoles. I will then explain the function of each organelle. Next, their differences: 1. Plant cells have a cell wall, but animals cells do not 2. Plant cells have chloroplasts, but animal cells do not 3. Plant cells usually have one or more large vacuole(s), while animal cells have smaller vacuoles I will also explain the function of each, and why animals don't have or need them, ex. plants have chloroplasts because they enable them to photosynthesize to make food, and animals do not photosynthesize because the amount of energy that photosynthesis would give animals is nowhere near enough what they need to be alive. Plants can survive on the minimal energy from the sun because they are still.

### Subject: Algebra

Simplify the following algebraic expression: 3(x + 7) + 2(-x + 4) + 5x

Well, first I would begin by introducing what the distributive property is. This will explain why the 3 and 2 get multiplied by what's in their adjacent parentheses. Next, I will introduce the concept of 'like terms,' which will help explain why we can combine 5x, -2x, and 3x. 3(x + 7) + 2(-x + 4) + 5x ---> (original) = 3x + 21 - 2x + 8 + 5x ----> (expanded, distributive property) = (3x - 2x + 5x) + (21 + 8) ----> (combine like terms) = 6x + 29 ----> (final answer)

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