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A soft drink manufacturer requires services of your software house to automate the process of can designing. The available material for the bottom and top of the can cost 20cents/cm^2. and for the sides the material cost is 10cents/cm^2. The company is considering two design options; one design does not include the lid and is an open top design, and the other design includes the lid and thus is a closed top design. The company wants your software house to provide them with a MATLAB code which will take desired volume, and design (open top or closed top) as input and give dimensions and surface area of the can that will result in the minimum cost as output for the specified volume and design. To test your code the company has asked you to use 275cm^3 as volume for both designs. Furthermore, if the budget of the company is $2 million, how many cans of the required design will the company be able to make?
A boat is pulled into a dock by means of a rope attached to a pulley on the dock, Figure 2.1. The rope is attached to the bow of the boat at a point 1 m below the pulley. If the rope is pulled through the pulley at a rate of 1 m/sec, at what rate will the boat be approaching the dock when 10 m of rope is out
A hamburger wrapper is thrown from a third floor dorm window, and its motion can be modeled by the equation h(t) = -3t^2 + 6t + 30, where h is the height in feet and t is the time in seconds.
a. Find the vertex of the parabola, then describe what it tells us physically about the situation.
b. Find the x-intercept, then describe what it tells us physically about the situation.
Suppose f(x)={kx + 7 ; x>= 2 ,x^2+19 ; x < 2' , For what value of k is lim x→2 f(x) defined?
Q. Write down 10 uses of Surface Integration in computer science Engineering
For the following functions:
(a) f(x)=(x+2)²(x-1)
(b) f(x)= (x²)/(x²-9)
(c) f(x)= (x²-2x+1)/(x+1)
i. Find the critical numbers off (if any);
ii.Find the open interval(s) on which the function. increasing or decreasing
iii. Apply the first derivative test to identify all relative extrema;
iv. Use graphing utility to confirm your results.
Consider the function f(x)=sin x cos x+5 on the interval (0, 2pi).
(a) find the open interval(s) on which the function increasing or decreasing, and
(b) apply the first derivative test to identify the relative extrema.
Determine the open intervals on which the graph of f(x)= (x²)/(x²+1) is concave upward or concave downward
Find the points of inflection and discuss the concavity of the graph of the function
f(x)= (x+1)/√x
Find all relative extrema. Use the second derivative test where applicable.
(a) f(x)=√x2+1
(b) f(x)=cos x -x
#339914 on Dec 2023