In a rectangular axis system, what is the distance between the following points: A(24.4,30) and B(34.4,42.49) ?
Answer(s): A
First, draw a rectangular axis system and mark the two points.The easiest way to find the distance between them is to draw a triangle, where the line AB is the hypotenuse. You can see that the length of one side of the triangle is (34.4 – 24.4 = 10) and the other side is (42.49 – 30 = 12.49). The length of the line AB is received with the help Of the Pythagoras principle.
In a rectangular axis system, what is the area of a parallelogram with the coordinates: (5,7), (12,7), (2,3), (9,3)?
Answer(s): B
First, draw the axis system and mark the 4 points. Connect the points to get a parallelogram. The area is calculated by the multiplication of one on of the bases and the height. The height is (7 – 3 = 4), the length of the base is (9 – 2 = 7). The area is 4 x 7 = 28.
If the radius of a cylinder is doubled and so is the height, what is the new volume of the cylinder divided by the old one?
The volume of a cylinder is (pie x R2) x (height of cylinder). The new volume is (4 x 2 = 8) bigger.
If the radius of a cylinder is doubled and so is the height, how much bigger is the new lateral surface area (without the bases)?
Answer(s): D
The lateral surface area of a cylinder is (2 x pie x R) x (height of cylinder).The new lateral surface area is (2 x pie x 2R) x (double the height) = 4 times bigger.
1. If X ~ Y = X2 + XY, then what is the value of -1 ~ 2 ?
-1 ~ 2 = (-1)2 + (-1)2 = -1.
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