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Tutor profile: Maia C.

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Maia C.
Recent college graduate with a passion for math and English
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Questions

Subject: Economics

TutorMe
Question:

Does the production function Q = 3K^.5 * 2L^2 have constant, decreasing, or increasing returns to scale?

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Maia C.
Answer:

One way to determine if there are increasing, decreasing, or constant returns to scale in a production function is to substitute in a constant value for all inputs, then double that input, and compare the difference in output to the difference in input. For simplicity, let's start with inserting 1 into our equation as both our units of capital and units of labor, This yields: Q = 3(1)^.5 * 2(1)^2, which simplifies to 3(1) * 2(1), or 6, which is our units of output. Now, I'm going to double the units of both labor and capital and use 2 instead of 1, creating the equation Q = 3(2)^.5 * 2(2)^2, which simplifies to 3(1.4142136) * 2(4), which equates to 4.24264 * 8, which comes out to approximately 33.9411, which is Q, or units of output for this equation. Now, when we doubled our input from 1 to 2, we more than doubled our output from 6 to a bit over 33. In fact, the output increased by just over a factor of 5.6 (We can determine this by dividing our second value for Q (33.9411) by our first value of Q (6). Because doubling our units of input more than doubled our units of output, this production function exhibits increasing returns to scale.

Subject: English

TutorMe
Question:

What is the participle in the following sentence: 'Looking along the shoreline, Allie noticed several small crabs and seashells.'?

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Maia C.
Answer:

The participle here is "looking", and it is serving as an adjective modifying the noun of this sentence, "Allie". Because our participle ends in '-ing', it is a present participle, as opposed to a past participle, such as "looked".

Subject: Algebra

TutorMe
Question:

In the system of equations 3(x) + 5(y) = 38 6(x) + 2(y) = 44 What are the values of x and y?

Inactive
Maia C.
Answer:

I'm going to solve this equation using the substitution method. I'll start with 6x + 2y = 44 because I notice that the coefficient of y (2) is a common factor in all of the terms in this equation. So I'll subtract 6x from both sides, leaving the equation: 2y = 44 - 6x. Next, I'll divide both sides of the equation by 2 (2y/2 = (44 - 6x)/2), leaving y = 22 - 3x. Now that I have a single y term isolated, I'll substitute 22 - 3x into our other equation (3x + 5y = 38) in place of y. This will take 3x + 5y = 38, and leave 3x + 5(22 - 3x) = 38. I'll distribute the 5 into the parenthetical term, making the equation read 3x + 110 - 15x = 38, which simplifies to -12x + 110 = 38. Next, I'll subtract 110 from both sides of the equation, leaving -12x = -72. Finally, I'll divide both sides of the equation by -12, leaving x = 6. Now that we know x = 6, that value can be substituted into either of the original equations to find the value of y. I'm choosing to use 6x + 2y = 44. Because I know x = 6, I now have 6(6) +2y = 44, which becomes 36 + 2y = 44. Subtracting 36 from both sides leaves 2y = 8, and dividing both sides by 2 leaves y = 4. Just to double-check I have correct values, I'm going to substitute x= 6 and y = 4 into the other equation given at the beginning of this problem, to make sure the values still work. So 3x + 5y = 38 becomes 3(6) + 5(4) = 38. This simplifies to 18 + 20 = 38, which is correct.

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