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# Tutor profile: Sarah G.

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Sarah G.
M.S. Mechanical Engineering
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## Questions

### Subject: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?

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Sarah G.

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

### Subject: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\$\$?

Inactive
Sarah G.

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

### Subject:Algebra

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Question:

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

Inactive
Sarah G.

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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