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A trough is 4 meters long, 1.5 meters wide, and 2 meters deep. The vertical cross-section of the trough parallel to an end is shaped like an isoceles triangle (with height 2 meters, and base, on top, of length 1.5 meters). The trough is full of water (density ). Find the amount of work in joules required to empty the trough by pumping the water over the top. (Note: Use as the acceleration due to gravity.)
A car leaves Lima at noon traveling due West at 65 mph. At 2 PM, a car 300 miles south of Lima heads towards Lima at 70 mph. How quickly is the distance between the cars changing at 4 PM?
Find the volume of a solid that is generated by rotating the region formed by the graphs of y=x^2, y= 2, and x = 0 about the y-axis?
Discuss the pros and cons for Lagrange interpolations. Be sure to provide specific examples of both pros and cons, and include citations and references for all sources used.
Find the exact length of c in simplified radical form.
Probability Let A and B be two mutually exclusive events of a sample space S. If P(A) = 0.6 and P(B) = 0.2, find each of the following probabilities of
Determine the vertical and horizontal asymptotes and sketch the graph of the rational function F. Label all intercepts and asymptotes.
Calculate probabilites of gettin from 0 to 5 clubs on a hand. What is the probabilty of gettin 2 or fewer cubs of 5 cards?
For the problem, refer to the linear transformation T: R^3 --> R^3 given by T(x) = T(x, y, z) = (2x + 2z, x - y + z, 2x + 2z). Write the change of basis matrix K from the basis F of R^3 which consists of the eigenvectors
The monthly incomes of trainees at a local mill are normally distributed with a mean of $1,100 and a standard deviation of $150. find the probability that a randomly selected employee earns less than $900 a month.
Boris races his bicycle for 264 feet . A wheel of his bicycle turns 44 times as the bicycle travels this distance. What is the diameter of the wheel?
A kite 100ft above the ground moves horizontally at a speed of 8fts. At what rate is the angle between the string and the horizontal decreasing when 200ft of string have been let out?
A pool measuring 20 meters by 24 meters is surrounded by a path of uniform width. If the area of the pool and path combined is 1596 square meters, what is the width of the path?
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