Question 14A box with a square base and open top must have a volume of 87808 cm?. We wish to find the dimensionsof the box that minimize the amount of material used.First, find a formula for the surface area of the box in terms of only a, the length of one side of the squarebase.A(z) =Next, find the derivative, A'(x).= (2),VThe critical value is aThe function is Select an answer v until the critical value, and Select an answer v after, so the criticalvalue corresponds to a local Select an answer v

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Answered: Question 14 <. A box with a square base…

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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Suppose you are trying to approximate the volume of the moon. You approximate the radius to be 1,740 kilometers, but you suspect there may be an absolute error in your measurement of up to 35 kilometers. You know that the moon is approximately spherical and that the volume of a sphere is given by the equation V =4/3èr^3. If you calculate the volume of the moon using your approximation of the radius, what is the largest possible relative error in volume you might obtain?
A pool with a semicircular cross section is conceivable as follows. Suppose the length of the pool is L = 10, the cross-sectional radius of the pool is r = 1 and the volume of water that surrounds the pool is V = 12.4; Find the depth of water using Fixed point method with an accuracy of 10 ^ -5 .
5. (a) A company manufactures cylindrical metal drums with open tops with a volume of lcubicmeter. What should be the dimensions of the drum in order to use the least amount of metal in their production?
Find the slope and the equation of the tangent line to the curve. y = 2x^2 – 2x + 4 at (1, 4) Using the delta method: 1. In the given equation, replace x with x + ∆? and y with y + ∆?.2. Find ∆? by subtracting the given equation from the equation obtained in step1. Simplify.3. Divide both sides of the equation obtained in step2 by ∆?. Simplify.4. Find the limit as ∆? → 0 (zero).
Graph the two equations f(x)= 0.1x^2+0.5 g(x)= -0.1x^3+4x and find the volume if the cross sections perpendicular to the x-axis that are equilateral triangles
A box with a square base and open top must have a volume of 108 cm. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. Simplify your formula as much as possible. A(z) = Next, find the derivative, A’(x). A' (x) = Now, calculate when the derivative equals zero, that is, when A'(x) = 0. A' (x) = 0 when x = We next have to make sure that this value of x gives a minimum value for the surface area. Let's use the second derivative test. Find A"(x). A"(x) = Evaluate A"(x) at the x-value you gave above. NOTE: Since your last answer is positive, this means that the graph of A(x) is concave up around that value, so the zero of A'(x) must indicate a local minimum for A(x).
A company decides to change its floor plan from cubicle to open office. This will bring in a constant stream of $1,000 in extra income annually. If the company invests this extra income in an account that earns 2.5% continuously compounded interest for ten years, is it worth the change? The change in floor plan costs $7,000.

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