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Sarah G.

M.S. Mechanical Engineering

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Basic Math

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Question:

Sarah works at a grocery store making $8.25 an hour. In one week Sarah worked 2 hours on Monday, 5.5 hours on Wednesday and 3 hours on Thursday. Income tax is 15%. What is Sarah's net income that week?

Sarah G.

Answer:

First, we total the number of hours that Sarah worked in the week: $$2+5.5+3 = 10.5$$ hours. We take her hourly pay and multiply it by her total hours to determine her income before taxes: $$ 8.25*10.5 = 86.63$$. This value was rounded to the nearest cent. Finally we subtract the income tax: $$86.63-0.15*86.63 = 0.85*86.63 = 73.64$$. At the end of the week Sarah's net income is $73.64

Calculus

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Question:

What is the derivative of the following expression: $$f(x) = 5x^2+sin(2x)-e^{5x}+(3x+2)^3$$?

Sarah G.

Answer:

The derivative is : $$f'(x) = 10x+2cos(2x)-5e^{5x}+9(3x+2)^2$$

Algebra

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Question:

What are the points of intersection of $$y = x^2$$ and $$y = 4*x$$?

Sarah G.

Answer:

In order to find the points of intersection, the two expressions for $$y$$ can be set equal to each other: $$x^2 = 4*x$$. This can be rearranged and factored in order to determine the x locations in which the expression is valid: $$x^2-4*x = 0$$ becomes $$ x(x-4) = 0$$. Finally the expression on the left hand side equals 0 when x is 0 or 4. To determine the y coordinate, both x-coordinates can be plugged into the original expressions for y i.e. $$y=x^2$$ or $$y = 4*x$$. The points of intersection are therefore (0,0) and (4,16)

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