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Let F= (2 x, 2 y , 2 x + 2 z). 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 F as well as the value of the integral
linear word problem: In a week, the first car gets an average of 20 mpg, the second gets 25 mpg; the two cars combined drive a total of 1175 miles in that week, for a total gas consumption of 50 gallons.
What is the ant's linear velocity? Include appropriate units in your answer.
Statistics or Probability re Jukebox Scenario, On a Jukebox with 2000 songs, what is the probability that a single song will play during a 1 hour period, a 3 hour period
Find the equation of the circle with center at the intersection of 4x + y - 4 = 0 and x - y - 6 = 0 and passing through (-1, -3). What is the equation of the circle passing through (12, 1) & (2, -3) and having its center on the line 2x - 5y + 10 = 0..
how green theorem is applicable in finding the area of region? use green's theorem to calculate the area of the region between the x-axis and one arch of the cycloid with parametric equations x=a(t-sint), y=a(1-cost)
A package can have a maximum combined length and girth of 108 inches. Find the dimensions of the package of maximum volume that can be sent. (assume that the cross section is a square)
A company's costs, in millions of dollars, are given by the equation, C = x2 - 3x - 27, where x is the number of items sold, in thousands. What are the costs when 1,000 items are sold? 1,500 items?
Probability values.
Let n >= 2 be a number. Define the graph L2(n) as follows: Vertices are ordered pairs from the set {1, ..., n}. Two vertices are adjacent if they have the same first coordinate, or the same second coordinate (but not both).
the wheel revolves at a rate of πrad/min and the observer's line of sight with a specific seat on the Ferris wheel makes an angle Ø with the horizontal. at what time during a full revolution is Ø changing most rapidly?
At each trial of a game, Don and Greg flip biased coins, simultaneously but independently. For each trial, the probability of heads is pD and pG for Don and Greg, respectively.
A right triangle is a triangle with one angle measuring 90? In a right triangle, the sides are related by Pythagorean Theorem, , where c is the hypotenuse (the side opposite the 90?angle).
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