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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
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.
The hypotenuse of a right triangle is 8 cm long One leg is 2 cm longer than the other Find the length of the longer leg?
Suppose the longer leg is x cm. Then the shorter leg is (x-2) cm. So, by Pythagoras's theorem, x2 + (x - 2)2 = 82 ie x2 + x2 - 4x + 4 = 64 or 2x2 - 4x - 60 = 0 or x2 - 2x - 30 = 0 so x = 1 + sqrt(31) = 6.568 cm
A square green rug has a blue square in the centerthe side length of the blue square is x inches the width of the green band that surrounds the blue square is 6 inWhat is the area of the green band?
The side of the rug is 6+x+6 = 12+x inches. The area of the whole rug is (12+x)2 square inches. = 144+24x+x2 square inches. The blue square is x*x = x2 square inches. Which leaves the green band at 144+24x+x2 - x2 = 144+24x sq inches.
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 volume of the cube if the surface area is 96 square inches?
Suppose the length of each side is x inches. Then total surface area = 6*x2 sq inches. That is 6x2 = 96 so that x2 = 96/6 = 16 and so x = 4 inches. Therefore volume = x3 = 64 cubic inches.
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
What number comes next 101 95 83 74?
101 to 95 =-6 95 to 83 =-12 83 to 74 =-9 6 to 12 is x2 12 to 9 is -3 Therefore,-9x2 is -18 74-18=56 Ans: 56
How do you calculate the diameter of a rectangle?
A rectangle does not have a diameter, as such, but the diagonal is similar enough. If the sides of a rectangle are x cm and y cm then, using Pythagoras's theorem, the diagonal is sqrt(x2 + y2) cm.
How many square inches is a 10 inch diameter square?
It is easy to show this graphically but, given the limitations of this browser, an algebraic explanation is the best that I can do. Suppose the sides of the square are x inches. Then, by Pythagoras, the diameter is sqrt(x2 + x2) = sqrt(2x2) = x*sqrt(2) inches ie x*sqrt(2) = 10 or x = 10/sqrt(2) = 5*sqrt(2) Then area = x2 = 25*2 = 50 square inches.
What is the locus of all points in the plane 3 cm from a given segment?
5-3/x2-0x
