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Use Stokes' theorem to evaluate the integral of around the curve consisting of the straight lines joining the points (1,0,1), (0,1,0) and (0,0,1). In particular, compute the unit normal vector and the curl of as well as the value of the integral
she suggests building fences described by y=4x2 and y=x2+5. Farmer Jones thinks this would be much harder than just building an enclosure with straight sides, but he wants to please his wife. What is the area of the enclosed region?
Find the gradient of the function and the maximum value of the directional derivative at the indicated point:
A=(LP)/2-L^2, gives the area of a rectangle of perimeter P and length L. Suppose that you have 600 feet of fencing which you plan to use to fence in a rectangular area of land.
Find the probability for the serum cholesterol level.
Evaluate the tangent line approximation of the two values and compare with the true value - what about the graph cases
A one compartment vertical file is to be constructed by bending the long side of an 8 inch by 20 inch sheet of plastic along two lines to form a U shape. How tall should the file be to maximize the volume that it can hold?
police find the skeleton in an area where a woman slightly over 5ft(60 inches)tall is missing for over a year. can the partial skeleton be the missing woman?show work for h.
a 6 ft ladder is leaning against a wall. If the bottom of the ladder moves away from the wall at a speed of 3 ft/s, how fast is the midpoint of the ladder falling (towards the ground) when the bottom of the ladder is 3 ftaway from the wall?
Destiny shows her friend Kaitlyn a deck of cards. Assuming the cards are randomly distributed, what is the probability that Destiny draws an ace and does not replace it, and then draws another ace?
If 3 J of work are needed to stretch a spring from 12 cm to 14 cm and 5 J are needed to stretch it from 14 cm to 16 cm, what is the natural length of the spring?
A chemist has two alloys, one of which is 5% gold and 20% lead and the other which is 30% gold and 40% lead. How many grams of each of the two alloys should be used to make an alloy that contains 34 g of gold and 104 g of lead?
Using the washer method, find the volume of the solid generated when the region bounded by the curves y=(square root of)x and y=x^2 is revolved about the x-axis.
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