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Miranda N.

College Math Major

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Basic Math

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Question:

Solve for x: x=2(3*5)-2$$^2$$+7.

Miranda N.

Answer:

By following PEMDAS, we would simplify within the parentheses first, leaving x=2(15)-2$$^2$$+7. Next we would solve the exponents, so x=2(15)-4+7. Multiplication would be next, simplifying to x=30-4+7. Finally, we can use the associative property to simplify the addition and subtraction, leaving x= (30-4)+7 = 26+7 = 33.

Calculus

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Question:

What is the derivative of f(x)=cos(5x)?

Miranda N.

Answer:

The derivative of cos(x) = d(x)*-sin(x). When we substitute 5x in for x in this equation, we get that the derivative of cos(5x) = d(5x)*-sin(5x). Since d(5x)=5, we can simplify our equation to show that the derivative of cos(x)=-5sin(5x).

Algebra

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Question:

What is the slope of the line that goes through (3,4) and (8,2)?

Miranda N.

Answer:

We can find the slope of a line using the following equation: m = $$\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}$$. By substituting 2 for $$y_{2}$$, 4 for $$y_{1}$$, 8 for $$x_{2}$$, and 3 for $$x_{1}$$, we can determine that m = $$\frac{2-4}{8-3}$$, which simplifies to m = $$\frac{-2}{5}$$. So, the slope of this line is $$\frac{-2}{5}$$.

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