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The Laplacian of a function f of n variables x1, x2,⋯xn, denoted ∇2f is defined by ∇2f(x1, x2,⋯xn) := (∂2f/∂x12)+(∂2f/∂x22)+...+(∂2f/∂xn2)
Now assume that f depends only on r where r= (x12+ x22+⋯+x2n)1/2
i.e. f(x1,x2,⋯,xn)=g(r), for some function g
. Show that, for x1,x2,⋯,xn≠0, ∇2f=[(n-1)/r]g′(r)+g′′(r)
The acceleration of an object moving in a strange way has been modelled as a = exx .
a) Use integration by parts to find an equation to model the velocity if v = ∫ = exx dx
b) Is the problem any different if you find v = ∫ = xex dx
Give an example, USING YOUR OWN WORDS (NOT TEXT COPIED FROM THE INTERNET), of how either the Poisson or the Exponential distribution could be used to model something in real life (only one example is necessary). You can give an example in an area that interests you (a list of ideas is below). Give a very rough description of the sample space
Determine the equation of the plane containing the points P(1,3,2) Q=(-2,0,-2) and R=(1,4,3)
Find the parametric equations for the line L through P(5,-2,4) that is parallel to (1/2, 2, -2/3)
(i) where does line L intersect the xy- plane?
(ii) sketch the position vector for a and the line L.
1.Discuss the graph of the equation x^2 +y^2 + z^2 -6x +8y+4z+4=0
1. Find the midpoint of the segment with ends (4, -3, 1) and (-2, 5, 3).
2. Determine whether the vectors u=3i+j-2k and v=2i-4j+k are orthogonal.
3. Describe and sketch 9x^2 + 9y^2 - 4z^2=0
y''+2y'=0 find two power series of the given differential equation about ordinary point x=0.Compare the series of the solution with the solution of differential obtained using the method section 4.3.Try to explain any differences between the two forms of the solution.
The company made a profit before tax of Ksh. 14,000,080 in the past 12 months of accounting
-The company made a net book loss of Ksh.1,100,050 in the year 2019
-The company engaged in consultancy services in the year 2020 where they were paid Ksh. 5,000,000
-The company supplied vaatable goods worth Ksh. 3,500,000 and Ksh. 9,000,000 in the years 2019 and 2020 respectively
-The company is seeking to invest Ksh. 7,000,000 in the coming year in a foreign country and in a different line from what they are dealing with in Kenya
Required:
(I) Calculate the different taxes due from the company as at the close of the year 2020 (6 mks)
(ii) Advise the company concerning their planned investment in terms of the taxation concept of incvestment. (3 mks)
c) Explain the relevance of Ability to pay theory in Kenya as applied in the principle of taxation.
Let r=xi^+yj^+zk^ and r=||r||. Show that: ∇(lnr)=r/r^2 .
and
∇×(r^n r)=0.
