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Define a relation R on the set of all integers Z by xRy iff x+y = 3k for some integer k. Is R an equivalence relation on Z? Why or why not?
Let f be a function that is differentiable for all real numbers. The table gives the values of f and its derivative f' for selected points x in the closed interval -1.5 0 for -1.5
Heat Equation Problem, Find the solution u(x,t) of the heat equation: with initial data u(x,0) = x
Find a definite integral that represents the arc length of the curve over the indicated interval and observe that the length cannot be evaluated with the techniques studied so far
A cube has a sphere inscribed inside of it. It has another sphere circumscribed on the outside ot if (it being the cube). What is the ratio of the volume of the inside sphere to the volume of the outside sphere?
The problem that I'm having is that there is a nonconstant factor of (x^2+y^2+z^2)^(-1/2) appearing on the RHS of this equation, making it non-trivial to solve.
A particle is set in motion at time t=0 and moves to the right along the x-axis. (a) Suppose that its acceleration at time t is a=100e^(-1). Show that the particle moves infinitely far to the right along the x-axis.
Create a probability tree showing all marginal, conditional, and joint probabilities.
A basket contains 6 red apples and 9 green apples . A sample of 5 apples is drawn. Find the probability that the sample contains
Using the readings discussed in this course, provide one real-world application of the information learned that has been the most valuable to you. Why has it been valuable?
Is the surface integral of a closed surface (for example the surface is the cylinder x^2+y^2=9 between the planes z=0 and z=2, together with the top and the bottom) supposed to be 0?
Given the adjacency relation p = {(1,4), (1,5) (1,6), (6,2), (6,3), (6,5)} on the set N ={1,2,3,4,5,6}, find the corresponding directed graph and adjacency matrix.
One can of pumpkin pie mix will make a pie with a diameter of 8 in. If two cans of pie mix are used to make a larger pie of the same thickness, find the diameter of that pie. Use radical 2 is approximately 1.414.
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