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# Tutor profile: Pierre E.

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Pierre E.
Certified Tutor with advanced degrees in Math, AI, and Statistics
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## Questions

### Subject:SAT II Mathematics Level 2

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Question:

A circle has parametric equations $$x= 5cos(t)$$ and $$y = 5 sin(t)$$ , where t is the parameter. Find the diameter of this circle

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Pierre E.

1) Recall $$(x-h)^2 + (y-k)^2 = R^2$$ is the equation of the circle 2) Find $$x^2 =[5cos(t)]^2 =25cos^2(t)$$ 3) Find $$y^2 =[5sin(t)]^2 =25sin^2(t)$$ 4) therefore, $$x^2 +y^2 = 25cos^2(t)+ 25sin^2(t) = 25 [cos^2(t)+ 25sin^2(t)]$$ 5) Using the trig identity $$cos^2(t)+ sin^2(t) =1$$, we get $$x^2+y^2 =25$$ 6) Since $$R^2=25$$ , $$R = \sqrt25= 5$$ 7) Finally Diameter = 2 radius, hence diameter = 10

### Subject:SAT

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Question:

The diameter of a circle graphed in the xy-plane has endpoints at (-23,15) and (1,-55). Which of the following is an equation of the circle?

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Pierre E.

1) The formula for a circle with a center at (h,k) and a radius R is $$\ (x-h)^2 +(y−k)^2 =R^2$$ 2) Let's begin by finding the center. The center will be at the midpoint of the diameter. (I) The h-coordinate will be halfway between the two x-values of the diameter. $$\frac{-23+1}{2} =-11$$ (II) The k-coordinate will be halfway between the two y-values of the diameter. $$\frac{-55+15}{2} =-20$$ 3) The radius is the distance from the center to any endpoint. So, using the distance formula: $$R^2=(x-h)^2+(y-k)^2 = (-23--11)^2 +(15--20)^2 = (-12)^2 +(35)^2 = 1369$$ . 4) Let's put the center and the radius into our equation for a circle $$(x+11)^2+(y+20)^2 =1369$$

### Subject:ACT

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Question:

If the mean of the numbers {4, 16, 10, x, 8, 20} is 12, what is the difference between the mean and the median?

Inactive
Pierre E.

1) write the equation of the mean: (4+16+10+8+20+x)/6=12 or (58+x)/6=12 2) Solve for x: 58 + x =6*12 or 58 + x = 72 hence 58-58 + x = 72-58 hence x = 14 3) write the six numbers in ascending order: 4, 8, 10, 14, 16, 20 4) Find the median as (10 + 14)/2 =12 5) Compute the difference between the mean and the median: 12-12 = 0

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