(2) An open metal pan is to be made by cutting out squares of the same size from the cornersof a rectangular piece of metal 14 inches by 18 inches and turning up the sides.a) Find a mathematical model expressing the volume of the pan as a function ofthe length of the side of the square cut out.b) What is the domain of your function in part (a)?c) Prove that the function is continuous on its domain.

Remark: we know that the formula of volume of a cuboid is = Length × Width × Height.

Answered: (2) An open metal pan is to be made by…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. Determine the equation of: a. The cubic function with zeroes 1, -2, -5 and y-intercept 10. b. The quartic function with roots at 2 & -1, and a double root at 3, and through (4,-10)
Consider an axisymmetric feeding bowl as shown on the left below. Its cross-section is shown on the right with the axis of symmetry aligned along the y-axis. The top curve of the cross-section is given by the function b. What is the capacity of this bowl? Capacity= cm³ c. Find the volume of water inside the bowl if the water level is 3.3 cm measured from the bottom. Volume of water = 1 961 y = C 961 The horizontal base joins the endpoints of the top curve. Both x and y are in cm. You may need to use a computer algebra system to solve some of the following problems. Round all your answers to at least 3 significant figures. a. Assume that the bowl is solid and is made with plastic. Find the amount of plastic (as a volume) required to make this bowl. Amount of plastic = cm³ cm3 -x4 (9-x) 1 4 -x¹ (9 + x) y 0≤x≤9.1 -9.1 < x < 0 X
A rectangular package sent by a delivery service can have a maximum combined length and girth (perimeter of a cross section) of 120 inches. Determine which of the following functions gives the volume of the package. (Assume the volume is measured in cubic inches.) Approximate the dimensions of the package that yield a maximum volume. (Round your values to the nearest inch.)
The demand for Chavez Doodads is described by the function q = 20(4p - 3p)¹/4, where • Ps is the average price of a substitute for Chavez Doodads (measured in dollars) • p is the price of a Chavez Doodad (measured in dollars). . q is the monthly demand for Chavez Doodads, (measured in 1000s of units) əq Op p=4 P8=7 Əq (b) aps 8 p=4 P8=7 = -0.625 = 2.5

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