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Pre-Calculus
TutorMe
Question:

If $$sec(\theta)=\frac{5}{3}$$ and 0°<θ<90°, what is $$cos(θ)$$?

$$cos(\theta)=\frac{1}{sec(θ)}$$ so $$cos(\theta)=\frac{1}{\frac{5}{3}}=\frac{3}{5}$$

Calculus
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Question:

What is the derivative of $$f(x)=sin(3x)$$?

To take the derivative of this function requires the chain rule which states if $$f(x)=g(h(x))$$ then $$f'(x)=g'(h(x))* h'(x)$$. In this problem, $$g(x)=sin(x)$$ and $$h(x)=3x$$ so $$g'(x)=cos(x)$$ and $$h'(x)=3$$. Substituting these into the chain rule, $$f'(x)=cos(3x)*3=3cos(3x)$$.

Physics
TutorMe
Question:

A block of mass $$2.5 kg$$ is pushed $$2.2 m$$ along a frictionless horizontal table by a $$16 N$$ pushing force directed $$25^{o}$$ below the horizontal. Is the work done by the pushing force positive, negative, or zero?

The work done by the pushing force is positive because a component of the pushing force is in the direction of the mass's motion.

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