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What is x2-x-72 factored?
74
What is the size in cm if 2'x2'?
2x2x2.54x2.54=25.8064cm
A box with a square base and open top must have a volume of 32000cm3 find the dimensions of the box that minimize the amount of material used?
Suppose the sides of the base are x cm, and the height is h cm. Then the volume = x2*h = 32000 cm3 The amount of material used for the base and 4 sides (no top) is x2 + 4xh cm2 So the requirement is to minimise x2 + 4xh subject to x2h = 32000 or h = 32000/x2 So minimise x2 + 4x*32000/x2 or x2 + 128000/x Setting the derivative = 0, 2x - 128000/x2 = 0 or 2x3 = 128000 or x3 = 64000 or x = 40 cm. And then h = 32000/x2 = 20 cm.
What is the volume of the cube in cubic feet if the surface area of cube is 96 square inches?
If a cube has sides of length x inches, its surface area is 6*x2 sq inches. So 6*x2 = 96 x2 = 16 so that x = 4 inches = 4/12 feet = 1/3 ft. Then the volume is (1/3)3 = 1/27 cubic feet.
What is the area of a triangle when its shortest side is less than the other sides by 18.55 cm and 21.2 cm respectively showing brief details of your work?
Presumably it's a right angle triangle so use Pythagoras' theorem and let the hypotenuse be (x+21.2) the height be (x+18.55) and the base be x:- (x+21.2)2-(x+18.55)2 = x2 If: (x2+42.4x+449.44)-(x2+37.1x+344.1025) = x2 Then: -x2+5.3x+105.3375 = 0 Solving the above by means of the quadratic equation formula gives x a positive value of 13.25 So the dimensions are: hypotenuse 34.45 cm, height 31.8 and base 13.25 cm Area = 0.5*31.8*13.25 = 210.675 square cm
