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- A box with an open top is to be constructed from a rectangularpiece of cardboard with dimensions 14 in. by 22 in. by cutting outequal squares of side x at each corner and then folding upthe sides as in the figure. Express the volume V of the box as afunction of x.Find the area in which region lies in first quadrant bounded by v = ³√(u) , u-axis and line v = u - n. where n=744 . give geometrical representation.A layer of equal spheres is in the form of a square. The spheres are arranged so that each sphere is tangent to every one adjacent to it. In the spaces between sets of four adjacent spheres, other spheres rest, equal in size to the original. These spheres form in turn a second layer on top of the first. Successive layers of this sort form a pyramidal pile with a single sphere resting on top. If the bottomlayer contains 16 spheres, what is the height of the pile in terms of the common radius r of the spheres.
- Find positive Z* such that -Z* and Z* enclose the central 34% of the area under the Z curve. State result to 2 decimal places.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. Let x denote the length of the side of the square being cut out. Let y denote the length of the base.3) A piece of sheet metal is rectangular,5ft wide and 8ft long. congruent squares are to cut from its corners. The resulting piece of metal is to be folded and wielded to from an open top box. How should this be done to get a box of largest possible volume?
- Eight identical balls were placed inside a cubical box of side 84 such that every ball is in contact with the walls of the box and with the adjacent balls. Find the radius of the largest ball that can fit in the center of the eight ballsA cylinder has a diameter of 7 cm and a height of20.8 cm. It holds 3 balls each with a diameter of 6.9 cm.How much space is left in the can after the three balls are putin it?Find the area of one ‘loop’ of the curve r= 4sin(5θ)
- Use the Fundamental Theorem of Calculus, Part I to find the area of the region under the graph of the function ?(?)=9?−2on [1,2]. (Use symbolic notation and fractions where needed.) ?=Find the area of the region enclosed between y=3sin(x) and y=2cos(x) from x=0 to x=0.8π.Hint: Notice that this region consists of two parts.A rectangular box with a square base and no top is to be constructed. It must hold 32,000 in3. What are the dimensions of such a box that uses the smallest amount of material (i.e. that has the smallest surface area)?
