Serisha G.

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Geometry

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Question:

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

Serisha G.

Answer:

Let r be the radius of the semicircle. Area of the semicircle is known; hence 1250Pi = (1/2) Pi 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 = 5000cm^2

Basic Math

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Question:

Solve: 3(x+5) + 2 = -1

Serisha G.

Answer:

A. 3x + 15 + 2 = -1 B. 3x = -1 -2 -15 C. 3x = -18 D. x = -6

Algebra

TutorMe

Question:

A car travels from A to B at an average speed of 50 km/hour. At what average speed would it have to travel from B to A to average 60 km/hour for the whole trip?

Serisha G.

Answer:

Let d be the distance between A and B T1 = d / 50 : travel time from A to B Let S be the speed from B to A T2 = d/S : travel time from B to A 60 = 2d/(T1 + T2) : average speed for the whole trip 60 = 2d/(d/50 + d/S) : substitute T1 and T2 S = 75 km/hour : solve the above equation for S.

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