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Partial Derivatives
Partial derivatives are used while we want to investigate the effect of one independent variable on dependent variable. For illustration, the revenues of a farmer may depend on two variables that is; the amount of fertilizer applied and as well the type of the natural soil.
Assume ∏= 30x2y + y2 + 50x + 60y
Whereas ∏ = annual revenue in £ '000'
x = type of soil
y = amount of fertilizer applied
The product of -7ab and +3ab is (-7 x 3) a 2 b 2 = -21a 2 b 2 . In other words, a term with minus sign when multiplied with a term having a positive sign, gives a product having
If 65% of the populations have black eyes, 25% have brown eyes and the remaining have blue eyes. What is the probability that a person selected at random has (i) Blue eyes (ii) Bro
Find the Laplace transforms of the specified functions. (a) f(t) = 6e 5t + e t3 - 9 (b) g(t) = 4cos(4t) - 9sin(4t) + 2cos(10t) (c) h(t) = 3sinh(2t) + 3sin(2t)
Let a, b, c 2 Z + . (a) Prove that if a|b, then ac|bc for all c. (b) If a|bc, can you conclude that either a|b or a|c? Justify your answer with a proof or a counter example.
A radioactive substance decays to 30% of its original mass in 15 months. Determine the half-life of this radioactive substance to the nearest month
Consider the integral where the notation means a contour that is parallel to the real z axis, but moved down by a distance d . Use the method of steepest descents to deri
In the graphical representation of a frequency distribution if the distance between mode and mean is k times the distance between median and mean then find the value of k.
principal=2000 rate=5% time=2 years find compound interest
A parcel of land, value $250,000 is sold to an investor who signs a contract agreeing to pay a deposit of $25,000 followed by equal quarterly payments for as long as necessary, wit
Finding the Inverse of a Function : The procedure for finding the inverse of a function is a rather simple one although there are a couple of steps which can on occasion be somewh
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