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Integration Applications:
The ends of a horizontal water tank are parabolic. The tank is 9 feet tall and 6 feet across at the top. Find the fluid force on a parabolic end of the tank if the tank is 5 feet full. Assume that the water weighs 62.4 pounds per cubic feet.
M(dv/dt)= -cv-mg v(0)=0, find v(t) and check that your answer satisfies the initial condition and the differential equation.
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).
Suppose K is a conjugacy class of S_n (the symmetric group), with K consisting of even permutations. Suppose that x in K. Show that K splits into two conjugacy classes
The center of a circle inscribed in a triangle is the same point as the intersection of the triangle's _?_.
In Example 3 of Section 2.5, the text shows how to write a system of linear equations using matrix notation. You can similarly write a linear programming problem in matrix notation.
Imagine that a line on a Cartesian graph is approximately the distance y in feet a person walks in x hours. What does the slope of this line represent? How is this graph useful? Provide another example for your colleagues to explain.
Use logic to write the negation of the sentence: All the participants of this course are IT majors or are Math majors. (Use the basic logic laws.)
If the sales effect for period 5 is $125 million and the carryover effect is 0.25, calculate the total sales impact for period 5.
Write the expression in the standard form a + b i. First convert to rectangular form--- calculate the magnitude-- find reference angle--then the argument of z---
If this problem is too difficult, then perhaps you may solve an easier one, just to give me some direction please. The only example I have is the Riemann function for the telegraph equation
Evaluate the value of x for which the power series converges - determine whether or not it converges at the endpoints of that interval.
Write computer code to determine the steady state temperature at the five co-ordinates in the rectangular region: (a/4,b/4), (3a/4,b/4), (a/4,3b/4), (3a/4,3b/4), (a/2,b/2) using the first 100 terms of the series solution (n = 1 to 100).
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