The Box Problem Take an 8% x 11 sheet of paper and cut out 4 congruent squares (one from each corner) as shown belo...
A candy box is made from a piece of cardboard that measures 25 by 14 inches. Squares of equal size will be cut out of each corner. The sides will then be folded up to form a rectangular box. Find the length of the side of the square that must be cut out if the volume of the box is to be maximized. What is the maximum volume? 14 in. A square with a side of length of 2.88 inches...
A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides. a. Suppose the paper is 9"-wide by 12"-long, i. Estimate the maximum volume for this box? (Hint: Use your graphing calculator.) * cubic inches Preview ii. What cutout length produces the maximum volume? - inches Preview b. Suppose we instead create the box from a 7"-wide by 9"-long sheet of paper. i. Estimate the maximum volume for this box?...
8. (10pts) A rectangular filed is to be enclosed with a fence. One side of the field is against an existing wall, so that no fence is needed on that side. If material for the fence costs $2 per foot for the two ends and $4 per foot for the side parallel to the existing wall, find the dimensions of the field of largest area that can be enclosed for $1000, 9. (11pts) A candy box is made from a...
A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with dimensions 40 cm by 60 cm by cutting equal squares from the four corners and turning up the sides. Find the length of the side of the cut-out square so that the box has the largest possible volume. Also, find the volume of the box
A square piece of cardboard is formed into a box by cutting out 3-inch squares from each of the corners and folding up the sides, as shown in the following figure. If the volume of the box needs to be 126.75 cubic inches, what size square piece of cardboard is needed?
To create an open-top box out of a sheet of cardboard that is 6 inches long and 5 inches wide, you make a square flap of side length x inches in each corner by cutting along one of the flap's sides and folding along the other. Once you fold up the four sides of the box, you glue each flap to the side it overlaps. To the nearest tenth, find the value of x that maximizes the volume of the...
Please answer the questions using MATLAB Exercise 1 Dimensions of the Largest Box An open bols to be made rom ฮ rectangular poce of cardboard measuring 8 x48. The box s made by cutting o ual squares rom cach of its 4 corners and turning up the sides. Suggestion: you can try making one yourself with of paper) spare piece u8. 1. Let x be the side of a square removed from each corner. Express the volume v of the...
Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. (a) Draw several diagrams to illustrate the situation, some short boxes with large bases and some tall boxes with small bases. Find the volumes of several such boxes. (b) Draw a diagram illustrating the general situation. Let...
The Problem: Depress the equation r6r +100 1. Decomposing a cube: Consider a cube with side length (a) Suppose we break the side of the cube at an arbitrary point ryb. This cut triggers the decomposition of the cube into the 8 pieces you have with your manipulative. You will have a cube with side length y and a cube with side length b. Identify the other 6 solids in terms of their dimensions using y and b so that...
Name: 1. For the function f(x) = x2 – 1 find and simplify: a. f(-2) b. f(-x) c. -f(x) d. f(x - 2) 2. Find the domain of each function below. Write your answer in interval notation. a. f(x) = x + 2 x2 + x - 6 b. 8(x) = (2x - 1 1 f(x + h) - f(x) 3. For the function f(x) = 2x2 – 3, find the difference quotient h 4. Use the graph of the...