rates, Mathematics

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Gauss-siedel or newton-rapson method, A one-line diagram of a simple three-...

A one-line diagram of a simple three-bus power system is shown in Figure 1 with generation at bus 1. The magnitude of voltage at bus 1 is adjusted to 1.05 per unit. The scheduled l

Logarithems , y=x4/4lnx-x4/16 then dy/dx=? Solution) dy/dx=-x^3/4(2/lnx-...

y=x4/4lnx-x4/16 then dy/dx=? Solution) dy/dx=-x^3/4(2/lnx-1)^2.    ^ means power

Fermat''s theorem, Fermat's Theorem : If  f ( x ) contain a relative extre...

Fermat's Theorem : If  f ( x ) contain a relative extrema at x = c & f ′ (c ) exists then x = c is a critical point of f ( x ) . Actually, it will be a critical point such that f

Triangles, if P is a point in the interior of a triangles ABC,prove that AB...

if P is a point in the interior of a triangles ABC,prove that AB>BC+CA

Solid mensuration, given dimensions: 130cm, 180cm, and 190cm is to be divid...

given dimensions: 130cm, 180cm, and 190cm is to be divided by a line bisecting the longest side shown from its opposite vertex. what''s the area adjacent to 180cm? ;

Step functions, Before going to solving differential equations we must see ...

Before going to solving differential equations we must see one more function. Without Laplace transforms this would be much more hard to solve differential equations which involve

Prove gcd value, Let a, b, c 2 Z + . (a) Prove that if a|b, then ac|bc f...

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.

PDE, Consider the wave equation utt - uxx = 0 with u(x, 0) = f(x) = 1 if-1 ...

Consider the wave equation utt - uxx = 0 with u(x, 0) = f(x) = 1 if-1 ut(x, 0) = ?(x) =1 if-1 Sketch snapshots of the solution u(x, t) at t = 0, 1, 2 with justification (Hint: Sket

How much is the volume increased, If the lengths of all sides of a box are ...

If the lengths of all sides of a box are doubled, how much is the volume increased? a. 2 times b. 4 times c. 6 times d. 8 times d. The volume of a box is taken by mu

What is the probability in which the marble chosen is blue, A bag holds 3 r...

A bag holds 3 red, 6 blue, 5 purple, and 2 orange marbles. One marble is selected at random. What is the probability in which the marble chosen is blue? The probability of blue

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