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Q1: Find three positive numbers whose sum is 54 and whose product is as large as possible
Q2: Let f(x, y) = x2 + 3y - 3xy and R is the triangular region with vertices (0, 0), (2, 0) and (2, 2). Find the interior and boundary points only at which the absolute extrema of f(x, y) can occur.
Given f(x,y,z)=x^2y^3z^6, in what direction is F(x,y,z) increasing most rapidly at the point P(1,-1,1). What is the rate of increase?
An orchard contains 50 peach trees with each tree yielding an average of 58 peaches. For each 4 additional trees planted, the average yield per tree decreases by 12 peaches. How many trees should be planted to maximize the total yield of the orcha..
A bag contains three red marbles, three green ones, one lavender one, two yellows, and four orange marbles. How many sets of five marbles include either the lavender one or exactly one yellow one but not both colors?
Hypothesis testing for single mean.
A plane flying with a constant speed of 390 km/h passes over a ground radar station at an altitude of 2 km and climbs at an angle of 30 degrees. At what rate is the distance from the plane to the radar station increasing a minute later? (Round you..
Use Taylor's expansion to arrange the function in ascending order - explain briefly how the Taylor expansions tell you what order the functions
A pole 70 feet tall is situated at the bottom of a hill that slopes up at an angle of 9.9 degrees. A guy wire fromthe top of the pole to the hillside forms an angle of 25 degrees eighths top of the pole. Find the distance of the pole to the guy wi..
What must be true for a pentagon so that it will tessellate a plane?
If 4 Americans, 3 Frenchmen and 3 Englishmen are to be seated in a row, how many seating arrangements are possible when people of the same nationality must sit next to each other?
A motel has 20 rooms. If the manager charges $60 per room per night, all the rooms will be rented. For each $5 increase, one less room will be rented.
A particle is moving along the curve y= 3 sqrt{4 x + 9}. As the particle passes through the point (4, 15), its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance from the particle to the origin at this ..
The average grade on a midterm exam in a certain math class was an 88. Is this a parameter or a statistic?
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