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# Tutor profile: Emily B.

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Emily B.
Grad Student with Over Three Years of Tutoring Experience
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## Questions

### Subject:Pre-Calculus

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Question:

Simplify the following. Write your answer in standard form. (4 + 5i) / (-6i)

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Emily B.

When dealing with complex numbers, standard form is always a + bi. In standard form, i cannot be in the denominator, so we start by multiplying both the numerator and denominator by the conjugate of -6i (which is 6i) [(4 + 5i)(6i)] / [(-6i)(6i)} In the numerator, we must distribute the 6i onto both terms. And in the denominator, we multiply the -6 times the 6 and the i times the i to get: (24i + 30i^2) / -36i^2 By definition, i^2 is equal to -1 (24i +30(-1)) / (-36)(-1) (24i - 30) / (36) Now, we can divide each term in the numerator by 36 and then we'll simplify to get the expression in standard form 24i/36 - 30/36 (2/3)i - (5/6) Now, we just need to switch the order of the terms to conform fully to the a + bi pattern. Thus, our final answer is: (-5/6) + (2/3)i

### Subject:Calculus

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Question:

A spherical balloon is inflated with gas at a rate of 800 cm3/min. How fast is the radius of the balloon increasing when the radius of the balloon is 30cm?

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Emily B.

### Subject:Algebra

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Question:

Solve the equation |-4x + 3| - 4 = 13

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Emily B.

|-4x + 3| - 4 = 13 To isolate x, we want to slowly "move" all non-x elements to the other side of the equal sign Start by adding 4 to both sides (this effectively "moves" the -4 from the left to the right) |-4x + 3| = 17 Next, we need to think about what to do about that absolute value on the left. We know that the absolute value of (-4x + 3) = 17. This will be true in two scenarios. First when (-4x + 3) = 17, AND ALSO when (-4x + 3) = -17. So now we need to solve for both of those scenarios. SCENARIO 1: -4x + 3 = 17 Once again, think about "moving" all non-x entities to the opposite side of the equal sign. In this case, start by subtracting 3 from both sides. -4x = 14 Next, divide both sides by -4 x = 14/-4 This fraction can be simplified to: x = -7/2 = -3.5 SCENARIO 2: -4x + 3 = -17 Subtract 3 from both sides -4x = -20 Divide both sides by -4 x = -20/-4 This fraction can be simplified to: x = 5 (note that the answer is POSITIVE 5, since a negative divided by a negative is a positive) So we have our two answers, x = -3.5 and x = 5 The final step is always to double check our answers by plugging these values back into our original equation. CHECKING ANSWER #1: |-4(-3.5) + 3| - 4 = 13 |14 + 3| - 4 = 13 |17| - 4 = 13 17 - 4 = 13 13 = 13 CHECKING ANSWER #2: |-4(5) + 3| - 4 = 13 |-20 + 3| - 4 = 13 |-17| - 4 = 13 17 - 4 = 13 13 = 13

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