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The tank shown below is full of water. Using the fact that the density of water is 1000kg/m3, find the work (in joules) required to pump the water out of the outlet. Make sure your answer is correct to within one thousand joules. Hint: Evaluate the integral by interpreting part of it as the area of a circle.
Suppose V is a complex inner product space and T: V --> V a linear operator. Use the results from parts (a) and (b) to show V = im(T) + ker (T*) = im(T*) + ker(T).
The side bordering the stream is not to be fenced. If 1000 yards of fencing material is to be used, what are the dimensions of the largest rectangular field that can be fenced. what is the maximum area.
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?
True or False: The graph of every equation of the form y = ax2 + b, where a and b are real numbers and a is not zero, is a parabola with the y-axis as the axis of symmetry.
a pool contains 125 gallons of water every minute an additional 25 gallons of water are added write an equation to describe the function.
Suppose that each time that you buy a car, you choose between Ford and General Motors. Suppose that each time after the first, you stay with the same company with probability 2/3 and switch with probability 1/3
In a random sample of 330 homes, what is the probability that more than 70 do not have an answering device? The probability that more than 70 do not have an answering device
Afton made a chicken dish for dinner. She added a 10- ounce package of vegetables and a 14- ounce package of rice to 40-ounces of chicken. What was the total weight of the chicken dish in pounds
What mass of H2O is produced when 0.400 moles of KOH react completely in the following equation?
What similarities and differences do you see between the functions and linear equations? 2) Are all linear equations functions? Is there an instance when a linear equation is not a function? Support your answer.
A homeowner wants to enclose a 5,800 square feet rectangular garden by a fence in his backyard. If three sides of the fence cost $6.25 per foot and 4th side costs $10.25 per foot,
If the rope is pulled in at a rate of 1.4 m/s, how fast is the boat approaching the dock when it is 10 m from the dock?
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