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- Solve for y2 by using reduction of order And for nonhomogeneous using undetermined coefficients linear mathematicsAn open–top box with a square base is to be constructed from two materials, one for the bottom and one for the sides. The volume of the box must be 18 cubic feet. The cost of the material for the bottom is 4 pesos per square foot, and the cost of the material for the sides is 3 pesos per square foot. Find the dimensions of the box such that the cost is at its minimum. Find the domain of the function, the critical points and include the second derivative test.a) The equation of the horizontal asymptote. b) A critical point.
- A soda can needs to contain 355ml of liquid (note: 1ml=1cubic centimeter). What dimensions should be used to construct the can with the minimum amount of material? In the answer please include: •the optimizing function & its domain •supporting work to find minimizing material •dimensions needed to minimize the amount of material •verify answer using 1st or 2nd derivative Please show all workdivergent or convergent for both problem and could you please show whyA closed right circular cylinder will be built with two types of metal. The base and the top of the cylinder will be constructed of metal that has a value of $ 2 per cm2, while The side surface of the cylinder will be constructed of a metal that costs $ 2.5 per cm2. The function that allows to minimize the cost of manufacturing said cylinder is given by: the answers are in the first attached image
- obtain general and particular solution satisfying initial condition indicated using homogenous functionA parabola that passes through the point (6, 46) has vertex (-4, 6). Its line of symmetry is parallel to the y-axis. Find equation of the parabola: y = When x = 16, what is the value of y: What is the average rate of change between x = -4 and x = 16: (fraction, or decimal rounded to thousands; no mixed fractions)Find all the critical points and horizontal and vertical asymptotes of the function f(x)=(x^2+5)/(x-2). Use the First and/or Second Derivative Test to determine whether each critical point is a local maximum, a local minimum, or neither. You may use either test, or both, but you must show your use of the test(s). You do not need to identify any global extrema.