Advance Math question and answers for July 24, 2023
- Q 2. Find the volume of revolution by WASHER: ? = 2?^(1/2) ??? ? =x
- Q 8. Determine the centroid, ?(??,??,??), of the solid formed inthe first octant bounded by ?+??16=0 and 2?^2 ?2(16??)=0.
- Q Find a series solution ofy???xy?+ 2y= 0.
- Q Use Stoke's Theorem to find the circulation of F? =7yi? +3zj?+2xk? around the triangle obtained by tracing out the path (5,0,0)to (5,0,3) to (5,5,3) back to (5,0,0)
- Q 3. A machine is used to fill containers with a liquidproduct. Fill volume can be assumed to benormally distributed. A random sample of ten containers isselected, and the net contents(oz)...
- Q Denition:An orthogonal array OA(k, n) on n symbols is an n2 x karray such that, in any two columns, each ordered pair of symbolsoccurs exactly once.Prove that there exists an...
- Q 7) (a) (2 pts) How many permutations are there of the wordQUARANTINE?(b) (4 pts) How many of the permutations of QUARANTINE do NOTthe same letter appearing consecutively? (Thus, any permutationwith...
- Q C. Prove the following claim, using proof by induction. Showyour work.Let d be the day you were born plus 7 (e.g., if youwere born on March 24, d = 24...
- Q Graph theoryIn a certain school, there are 39 clubs and 194 students. Somestudents do not belong to any clubs but every club has at least onemember and no two clubs...
- Q A theater has 500 seats, divided into orchestra, main, andbalcony seating. Orchestra seats sell for $50, main seats for $35,and balcony seats for $25. If all the seats are sold,...
- Q The Main Street Entrepreneurship Kauffman Index is an indicatorof main street business activity, presenting trends in smallbusiness activity and ownership over the past two decades. Their2015 report stated that “reversing...
- Q Which of the following sets are rings with respect to the usualoperations of addition and multiplication? If the set is a ring, isit also a field? can you explain in...
- Q Let f(x, y) = xy3 ? x 2 + 2y ? 1. (a) Find the gradient vectorof f(x, y) at the point (2, 1).(b) Find the directional derivative of f(x,...
- Q ina class of 25 students, 17 passed calculus, 13 passed chemistry,and 8 passed physics. No one passed all three, but at least six ofthem failed all three subjects. How many...
- Q For each of the following problems (even the book ones) do thefollowing:a. Use the x- and y- nullclines to find all the equilibriumpoints.b. Compute the Jacobian matrix of the system.c....
- Q Let?F and?G be vector fields defined on R3 whose componentfunctions have continuous partial derivatives. Furthermore, assumethat ??×?F=??×?G.Show that there is a scalar function f such that?G=?F+??f.
- Q Solve the following initial value problem ut + 2ux ? 2u = e t+2x, u(x, 0) = 0
- Q Calculate each of the following (or indicate why it is notdefined) (a) (1,2,3,4) x (4,3,2,1) (b) (1,1,1) x [(1,2,3) x(3,3,0)] (C) (1,1,1). [(1,2,3) x (3,3,0) (d) (1,1,1) x [(1,2,3).(3,3,0)] (e)...
- Q Q1: Let x = [ x(t) y(t) ] and consider the system of ODEsx' = [5/2, 3; ?3/4 ,?1/2] x.(1)1.1 Solve the initial value problem subject to x(0) = 1,...
- Q The following are Trueor False statements. If True, give a simple justi?cation. If False,justify, or better, give a counterexample.1. (R,discrete) is acomplete metric space.2. (Q,discrete) is a compact metric space.3....
- Q 1. [25 marks] Consider the following model: maximize 40x1 +50x2subject to: x1 +2x2 ? 40 4x1 +3x2 ? 120 x1, x2 ? 0 The optimalsolution, determined by the two binding...
- Q Let D10 denote the dihedral group of the hexagon.Thus, D10 is generated by r and f withr10=f2=1 andfr=r-1f=r9f(a) Show that D10 has a subgroups N and M such thati. N...
- Q The determinant of a matrix is the product of its eigenvalues.Can you prove this when A is diagonalizable? How about if A is 2 x2, and may or may not...
- Q If G = (V, E) is a graph and x ∈ V , let G \ x be the graphwhose vertex set is V \ {x} and whose edges are...
- Q 1.a) The demand per week for television sets is 1200 units whenthe price is $575 each and 800 units when the price is $725 each.Find the demand equation for the...
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