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1. For a function f : Z → Z, let R be the relation on Z given by xRy iff f(x) = f(y).
(a) Prove that R is an equivalence relation on Z.
(b) If for every x ? Z, the equivalence class of x, [x], contains exactly one element, what can be said about the function f?
Explain the Graphical Technique of Linear Equations by using this figure.
solve the differential equation 8yk+2-6yk+1+yk=9 ,k=0 given that Y0=1 and y1=3/2
1. Use mathematical induction to prove whenever n is a positive integer. 2. Use loop invariant to prove that the program for computing the sum of 1,...,n is correct.
class 10 Q.trigonometric formula of 1 term
( a+2b)x + (2a - b)y = 2, (a - 2b)x + (2a +b)y = 3 (Ans: 5b - 2a/10ab , a + 10b/10ab ) Ans: 2ax + 4ay = y , we get 4bx - 2by = -1 2ax+ 4ay = 5 4bx- 2by = - 1
A garden shop wishes to prepare a supply of special fertilizer at a minimal cost by mixing two fertilizers, A and B. The mixture is to contain at least 45 units of phosphate at lea
what is the differeance in between determinate and matrix .
A dealer sells a toy for Rs.24 and gains as much percent as the cost price of the toy. Find the cost price of the toy. Ans: Let the C.P be x ∴Gain = x % ⇒ Gain = x
simplex methord
compare: 643,251: 633,512: 633,893. The answer is 633,512.
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