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Problem 1- Apply the operator ∇ to products of smooth scalar fields Φ, Ψ, vector fields u, v, and tensor fields A, B. Establish the identities
div(Φu) = Φdivu + (u, gradΦ)
grad(u, v) = (gradTu)v + (gradTv)u
div(ATu) = (divA,u) + A : gradu
Problem 2- Compute the derivate DG(A) for each of the following functions
G(A) = (trA)A
G(A) = ABA
G(A) = ATA
G(A) = (u, Au)A
A random sample of 48 days taken at a large hospital shows that averages of 38 patients were treated in the emergency room per day. The standard deviation for the population is four. Determine the 99% confidence interval of the mean number of patient..
the perimeter of a basketball court is 292 ft. The length is 40ft longer than the width. find the dimensions of the court.
assuming no loss of speed,what is the velocity of the particle after the ricochet? simplify your answer.
find the center and the radius of the circle with equation (4x^2+40x)+(4y^2-8y)=-20
Establish an equation to determine revenue.
Calculate the mean and the standard deviation of the total score?
A scale model of a museum made of cubic blocks. In my answer document sketch the view as it would appear from 2nd avenue.
Find the y-intercept of the line represented by the following equation. -2x + 2y = 16 and Write the equation of the line with slope -4 and y-intercept (0, -9)
Please provide your own real-world example from your work or life using the slope and y-intercept. What are the slope and y-intercept in your example?
Prove Let D be a nontrivial connected digraph. Then D is Eulerian if and only if od(v)=id(v) for every vertex v of D. Od means the outdegree of a vertex v of a digraph D. (is the number of vertices of D that are adjacent from v.
The height in feet for a ball thrown upward at 48 feet per second is given by s(t)=-16t^(2)+48t, where t is the time in seconds after the ball is tossed.
a rancher has 200 feet of fencing available to enclose two adjacent retangular corrals. Each corral is to be the same size. What dimensions for each corral will maximize the area enclosed by the two corrals?
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