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Q: You cut square corners with side lengths that are whole numbers from a piece of cardboard with dimensions 20 inches by 30 inches. You then fold the cardboard to create a box with no lid. Which of the
following dimensions will give you the greatest volume? A. 12 in. by 22 in. by 4 in. B. 10 in. by 20 in. by 5 in. C. 14 in. by 24 in. by 2 in. D. 10 in. by 24 in. by 6 in.
A: Suppose the squares you cut have side length x, [ then we have: Length of box base: 20 - 2x Width of box base: 30 - 2x Height of box: x Volume of box: V = x(20 - 2x)(30 - 2x) V = x(600 - 40x - 60x + 4x^2) V = x(600 - 100x + 4x^2) V = 600x - 100x^2 + 4x^3 dV/dx = 600 - 200x + 12x^2 Set that to zero: 12x^2 - 200x + 600 = 0 x = (-(-200) +/- sqrt((-200)^2 - 4(12)(600))) / (2*12) x = (200 +/-
sqrt(40000 - 28800)) / 24 x = (200 +/- sqrt(11200)) / 24 x = (200 +/- sqrt(11200)) / 24 x =~ 12.74 or 3.92 Since you want whole numbers, x = 13 or 4 If x = 13, V = -312, but a negative number doesn't make sense, so we'll ignore that If x = 4, V = 1056, so that's the maximum volume The dimensions are: Length of box base: 12 Width of box base: 22 Height of box: 4 By the way, this is calculus, not grade 8 math! ]
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User: You cut square corners with side lengths that are whole numbers from a piece of cardboard with dimensions 20 inches by 30 inches. You then fold the cardboard to create a box with no lid. Which of the following dimensions will give you the greatest volume? A. 12 in. by 22 in. by 4 in. B. 10 in. by 20 in. by 5 in. C. 14 in. by 24 in. by 2 in. D. 10 in. by 24 in. by 6 in.



Weegy: Suppose the squares you cut have side length x, [ then we have: Length of box base: 20 - 2x Width of box base: 30 - 2x Height of box: x Volume of box: V = x(20 - 2x)(30 - 2x) V = x(600 - 40x - 60x + 4x^2) V = x(600 - 100x + 4x^2) V = 600x - 100x^2 + 4x^3 dV/dx = 600 - 200x + 12x^2 Set that to zero: 12x^2 - 200x + 600 = 0 x = (-(-200) +/- sqrt((-200)^2 - 4(12)(600))) / (2*12) x = (200 +/- sqrt(40000 - 28800)) / 24 x = (200 +/- sqrt(11200)) / 24 x = (200 +/- sqrt(11200)) / 24 x =~ 12.74 or 3.92 Since you want whole numbers, x = 13 or 4 If x = 13, V = -312, but a negative number doesn't make sense, so we'll ignore that If x = 4, V = 1056, so that's the maximum volume The dimensions are: Length of box base: 12 Width of box base: 22 Height of box: 4 By the way, this is calculus, not grade 8 math! ]
Expert answered|thederby|Points 1216|

User: how to find a radius of a circle

Weegy: 1 Learn the formulas relating radius to circumference, area and diameter. [ If pi is a constant, area = a, circumference = c, diameter = d and radius = r, the formulas are: c =2 pi r a = pi r^2 d = 2 r 2 Notice what you already know about the circle. If you are expected to find the radius, you will already know the diameter, area or circumference. Choose the equation from step 1 that relates radius to the quantity you already know. 3 Divide the diameter by 2 to get r if you know the diameter. For example, if your circle has a diameter of 4, the radius is 4/2 = 2. 4 Divide the circumference by 2 pi to find the radius if you know c. it's impossible to write the exact value of pi, but for most problems 3.14 is a good enough approximation. So, if your circumference is 618, you would get r = 618 / 2 pi r = 618 / 2 x 3.14 r = 618 / 6.18 r = 100 5 Plug in the area to find the radius if you know the area. If a = pi r^2 then r = the square root (sqrt) of the area divided by pi, or to put it in mathematical script, sqrt(a/pi). So, if the area is 3.14, we get: r = sqrt(3.14 / 3.14) r = sqrt(1) r = 1 Read more: How to Find the Radius of a Circle | eHow.com ]
Expert answered|thederby|Points 1216|

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Asked 5/28/2012 3:40:18 PM
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