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Let F=(2x,2y,2z) . Use Stokes' theorem to evaluate the integral of F 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
A printed poster is to have a total area of 750 square inches with top and bottom margins of 6 inches and side margins of 2 inches. What should be the dimensions of the poster so that the printed area be as large as possible?
If a goat is tied on a 50 foot lead to a corner on the outside of a rectangular barn and the barn is 20 feet by 20 feet and the goat can not get into the barn nor is the barn a grazing area
If the colored glass transmits only half as much light per square foot as the clear glass does, what are the dimensions of the window that transmits the most light? (The perimeter is still 100 feet.)
Find the 99 percent confidence interval on the proportion of all such gloves that are shorter than nine inches.
Using the window setting to make a graph.
Find the dimensions of the rectangle of the largest area that has its base on the x axis and its other two vertices above the x axis and lying on the parabola y=8-x^2.
Find all of number for which the rational expression: (x+4) / (x^2 - 3x -10), is not defined. Explain your answer and add explanatory text for each line of algebra. What role does the numerator play and why?
Hits on a personal web site occur quite infrequently. They occur randomly and independently with an average of five per week.
Recurrence relations with complex characteristic roots
The number of bacteria N in a culture is given by the model N=250e^kt, where t is the time in hours, with t=0, corresponding to the time when N=250.
A football is thrown downward from a window in a tall building. Its position at time t in seconds is s=16t^2+32t, where s is in feet. How long to the nearest tenth will it take the ball to fall 175 feet?
Advantages and disadvantages of strategy I and strategy II for finding the occurrence of supernova problem - What are some possible strategies for solving this problem?
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