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Consider ∫R∫ xy dA, where R is the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1. Let us compute some Riemann sums. For any positive integer n we partition R into n2 little squares Rij each with sides 1/n long. Within each little square we evaluate the integrand at the point (x*ij, y*ij), which is the upper right corner.
(a) Find a formula for the Riemann sum
(b) Evaluate the formula
(c) Check your answer by evaluating the iterated integral.
A student receives test scores of 62, 83, and 91. The student's final exam score is 88 and homework score is 76. Each test is worth 20% of the final grade, the final exam is 25% of the final grade, and the homework grade is 15% of the final grade...
the census figures show that the average income for a family in a rural region is approximately 34860 per year. a
What is the definite integral in range 2pi to 0 of the function sin(x/4)^2*cos(x/4)^2.
A clinical trial for a new fertility treatment was provided to 250 women for a 10 year study perio~Investigators were interested in noting when women became pregnant for the first time (subsequent pregnancies were not an outcome of interest, only fir..
your management team believes they have identified a resource allocation problem within the manufacturing department.
If you start with an initial surplus of 1, what is the probability that you will be ruined by time 2 or before? Given ψ (6) = a, ψ (5) = b, ψ (4) = c, express ψ (7) in terms of a, b, c.
Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. The insurance company knows that, last year, the life expectancy of its
A jazz concert brought in $166,500 on the sale of 8,100 tickets. If the tickets sold for $15 and $25 each, how many of each type were sold?
(a) Find the x-intercept(s) of the graph of the equation, if any exist. (Work optional) (b) Find the y-intercept(s) of the graph of the equation, if any exist. (Work optional)
Suppose that f(0)=20 cells and the population is increasing at a rate of 12 cells/hour at that point. Find the values of a and b. According to this model, what happens to the yeast population in the long r.
the lifetime of a light bulb is normally distributed with a mean life of 1000 hours and a standard deviation of 30 hours. Find the probability that a randomly selected light bulb lasts longer than 1045 hours.
Vanilla Box Company is going to make open-topped boxes out of 17 × 16-inch rectangles of cardboard by cutting squares out of the corners and folding up the sides. What is the largest volume box it can make this way?
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