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Pablo S.

Math & Physics Tutor | Mechanical Engineer | Soccer Fan

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Pre-Calculus

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Question:

Can you determine the equation of a circle with radius 3 and center of $$(3,-4)$$ in under 2 minutes?

Pablo S.

Answer:

Equation of a circle in standard form is determined by the following formula: $$ (x-h)^2 + (y-k)^2 = r^2$$ where $$r$$ is the radius of the circle with center coordinates of $$(h,k)$$ Solution: $$(x - 3)^2 + (y- (-4))^2 = 3^2$$ $$(x-3)^2 + (y+4)^2 = 9 $$ (Final answer!) Pretty simple, right?

Trigonometry

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Question:

Can you solve for $$\theta$$ in under 3 minutes? $$\ (sin^2(\theta) + cos^2(\theta))/2 = sin(\theta) $$

Pablo S.

Answer:

Utilizing trigonometry formulas, we know that $$\ sin^2(\theta) + cos^2(\theta) = 1$$ $$\ (sin^2(\theta) + cos^2(\theta))/2 = sin(\theta) $$ $$\ 1/2 = sin(\theta) $$ $$ \theta = sin^{-1}(1/2) $$ $$\theta = \pi/6 $$ or $$ 30^o$$

Algebra

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Question:

Solve for x: $$ 2(4x + 5) - (2x + 4) = 10 $$

Pablo S.

Answer:

Use order of operations to solve for x. (Hint: PEMDAS) 1. Multiply the 2 by the (4x+5) $$ 2(4x+5) - (2x+4) = 10 $$ $$ 8x + 10 - (2x+4) = 10 $$ 2. Distribute the negative outside of the (2x+1) as follows: (Hint: positive * positive = positive | negative * negative = positive | positive * negative = negative) $$- (2x+4) $$ $$ -2x - 4 $$ 3. Keep adding/subtracting alike terms (Hint: add/substract x terms) $$ 8x + 10 - 2x - 4 = 10$$ $$ 6x + 10 - 4 = 10$$ $$ 6x + 10 - 4 = 10$$ $$ 6x + 6 = 10$$ 4. Subtract 6 from both sides of the equal sign: $$ (6x + 6) - 6= 10 - 6$$ $$ 6x = 4$$ 5. 6 is multiplied by x, therefore you need to divide by 6 into both sides. $$ 6x/6 = 4/6 $$ $$ x = 4/6$$ 6. Remember to simplify! $$ x = 2/3$$ (Final Answer!)

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