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A right triangle with legs of 5 and 12 is rotated about it's hypotenuse to form a solid which is pointed at two ends. What is the volume of that solid? (Exactly in terms of pi).
Let a be the permutation (1 2 3) in A_4. What is the order of the element (3, 7, a) in the group U(10) direct product Z_42 direct product A_4.
State the value of the discriminant and then describe the nature of the solution. What is the value of the discriminant?
Find the vertices, foci, length of the major axis and length of the minor axis of the elipse ((x-1)^(2))/(4)+((y-2)^(2))/(9)=1
In each of the following parts, you should simplify your answers where it is appropriate to do so. Write down the derivative of each of the functions
How many solution sets do systems of linear inequalities have? Must solutions to systems of linear inequalities satisfy both inequalities? In what case might they not? Use an example for discussion.
A specialty-freezer company has determined that the operating costs at one of its plants can be approximated by the function:
Student arrive at the Administrative Services Office at an average of one every 15 minutes, and their requests take on average 10 minutes to be processed.
Let K be a normal subgroup of G, and both K and G/K are simple. Show that either K is the only nontrivial proper subgroup of G, OR G is isomorphic to K x (G/K).
A graph is outerplanar if it can be embedded in the plane so that every vertex lies on the boundary of the exterior region. Prove the following:
Use Mad to compare simple moving & weighted moving average
Describe (in words) two different sets of people containing you as a member. Describe (in words) the complement of each set. Describe what people are not in either the original set or the complement set.
Let f(x,y) be an infinitely differentiable function. Suppose that Consider the surface z = f(x,y). Show that K(0,0) = f_xx(0,0) f_yy(0,0) - f_xy(0,0)^2.
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