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Aniket P.

Graduate student

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Geometry

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Question:

The semicircle of area 1250 π centimeters is inscribed inside a rectangle. The diameter of the semicircle coincides with the length of the rectangle. Find the area of the rectangle.

Aniket P.

Answer:

Let r be the radius of the semicircle. Area of the semicircle is known; hence 1250π = (1/2) π r2 (note the 1/2 because of the semicircle) Solve for r : r = 50 Length of rectangle = 2r = 100 (semicircle inscribed) Width of rectangle = r = 50 (semicircle inscribed) Area = 100 × 50 = 5000

Basic Math

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Question:

Malav sells ice cream for a living. On Wednesday his revenue was 1000 dollars. On Thursday, his revenue was 1200 dollars. Finally, on Friday, his revenue was 700 dollars. How much is Malav's revenue so far?

Aniket P.

Answer:

This is simple addition word problem, We have 1000$ for Wednesday, 1200$ for Thursday and 700$ for Friday We will just add them up, 1000$+1200$+700$= 2900$ Finally Malav's revenue is 2900$

Algebra

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Question:

Solve this quadratic equation:- 2x^2 +4x + 3=0

Aniket P.

Answer:

In the above question we cannot find factors , so we use the following formula:- X= -b +- (√b^2 -4ac) / 2a So from the equation we have a=2, b=4, c=3 X = -4+(16-24)/4 or X = -4-(16-24)/4 X = -3 or X = 2

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