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A water trough is 10 meters long and the cross-sections have the shape of an isosceles trapezoid that is 30 cm wide at the bottom and 80 cm wide at the top with a height of 50 cm. If the trough is being filled with water at the rate of 0.2 cubic meters per minute, how fast is the water level rising when the water is 30 cm deep? Area of a trapezoid is A=1/2(b1+b2)h. So volume of the trough is the area of the ends times the length.
Let E be a metric space, S a subset of E, and let f:E-R be the function which takes the value 1 at each point of S and 0 at each point of the complement of S. Prove that the set of points of E at which f is not continuous is precisely the boundary..
Evaluate the Riemann sum for f(x)=3-1x/2 x is greater than or equal to 2 and less than or equal to 14 with six subintervals, taking the sample points to be left end- points.
Round your final answer to nearest hundredth. Find the height of the tree if it casts a shadow of 35 feet and the angle of elevation to the top of the tree is 40°.
Among completed surveys how many different responses to this survey were possible?
The function f is differentiable on the interval [-1,1]. The table shows the values of f' for selected values of x. Sketch the graph of f, approximate the critical numbers, and identify the relative extrema.
Resource: The Practice of Public Relations textbook,University Library, Internet Select one of the following case studies located in The Practice of Public Relations.
find the exponential function of the form y=ae kx that goes through the points (0,4) and (2,9).show all your steps and use four decimal places.
use eulers method to calculate the first three approximations to the given initial value problemuse eulers method to
a motorboat can contain a constant speed of 38 mph relative to the water. the boat makes a trip upstream to a certain point in 42 minutes; the return trip is 34 minutes. what is the current?
Find whether the given information results in one triangle.
1. Let A be a non-empty set. Prove that if there exists an injection f : A -> N(natural numbers), then A is finite or countably infinite. 2. Prove that on the real line R, the collection of all closed intervals with rational endpoints is a countable..
Calculate its characteristic polynomial and its eigenvalues. Find the eigenvectors of A. Diagonalize the matrix A
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