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Draw the direction field for the subsequent differential equation. Draw the set of integral curves for this differential equation. Solution: y′ = y - x To draw direct
sin 4 x - sin x = 0
Find no. of non negative integral solutions x 1 +x 2 +x 3 +4x 4 =20 Solution) 140. Break them into prime factors . Put 4 = 2^2 and every variable will have factors in 2,3,5 with
WHAT DIVISION MEANS : Ask any primary school teacher which areas in arithmetic the children find very difficult. Division will probably top her list. This is not surprising. If y
Standardizing a Random Variable If X is a random variable with E(X) = m and V(X) = s 2 , then Y = (X – m)/ s is a random variable with mean 0 and standard deviatio
In the introduction of this section we briefly talked how a system of differential equations can occur from a population problem wherein we remain track of the population of both t
Assume that the amount of air in a balloon after t hours is specified by V (t ) = t 3 - 6t 2 + 35 Calculate the instantaneous
If roots of (x-p)(x-q) = c are a and b what will be the roots of (x-a)(x-b) = -c please explain? Ans) (x-p)(x-q)=c x2-(p+q)x-c=0 hence, a+b=p+q and a.b=pq-c
DEVELOPING AN UNDERSTANIDNG OF MULTIPLICATION : The most important aspect of knowing multiplication is to understand what it means and where it is applied. It needs to be first i
Write down a game each to teach children i) multiplication, ii) what a circle is, iii) estimation skills. Also say what you expect the child to know before you try to t
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