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1. Find the area of the region bounded by the graph of y = (x2 - 5x + 6)e2x and the x-axis.
2. Find the volume of the solid obtained when the region under the graph of y = sin-1(x/ 2) for 0 ≤ x ≤ 2 revolved around the y-axis.
how far downstream does the boater finally land? (Hint: if x is the cross- stream position of the boat and y is its downstream position, find an expression for dy/dx. Then solve for y(x)).
Simplify the following expression as much as possible: Assume that all variables represent positive real numbers.
Are closures and interiors of connected sets always connected? (Look at subsets of R2).
We would like to build such a network in order to minimize the total building and transportation costs, so that all demand is met. Formulate the problem as an integer programming problem.
rancher has feet of fencing to enclose a rectangular corral with a dividing fence parallel to one side. What dimensions will produce the largest total area?
By reading values from the given graph of f, use five rectangles to find a lower estimate and an upper estimate for the area under the given graph of f from x = 0 to x = 40.
Calculate the mean, variance, and standard deviation of this distribution.
The surface is defined by the equation x^2 - 2y^2 + z^2 +yz = 2. Write equations of the tangent plane and normal line to this surface at the point P(2, 1, -1)
Simulate 2000 coin flip experiments with a biased coin with "success" probability (chance of 1) p = 1/5. Plot an outcome of the proportion of successes with respect to the number of coin flips. Supply your code.
Kenya is reserving a room in a hotel in France where they use euros (€). The room charge is €75. Suppose the conversion rate is €1 = $1.298. What is the cost of the room in dollars?
at a point (x,y) on a metal plate is T(x,y)=4x2-4xy+y2. An ant on the plane walks around the circle of radius 5 centered at the origin. What are the highest and lowest temperatures encountered by the ants.
Evaluate the type of conic from the given equation - Indicate which type of conic each of the following represents.
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