Asked in Math and Arithmetic, Algebra, Calculus
How do you prove 2x powk plus 4x powk minus 1 equals x powk plus 1?
if you mean: 2x^k + 4x^k -1 = x^k +1 6x^k - x^k = 1 + 1 5x^k = 2 x^k = 2/5 cannot be solved further without more info. with 2 variables you must have 2 equations to solve further. ...
Asked in C Programming, C++ Programming
Write a program to s wap kth and k plus 1th element?
Assuming the elements are integer type... a[k] ^= a[k+1]; a[k+1] ^= a[k]; a[k] ^= a[k+1]; ...but if they are not integer type... temp = a[k]; a[k] = a[k+1]; a[k+1] = temp; ...
How do you find the LCM of k to the 2nd power k to the 2nd power-1 and k to the 2nd power minus 2k plus 1?
Factor them. k2 = k x k k2 - 1 = (k - 1)(k + 1) k2 - 2k + 1 = (k - 1)(k - 1) Combine the factors, eliminating duplicates. k2(k + 1)(k - 1)(k - 1) = k5 - k4 - k3 + k2, the LCM ...
Asked in Proofs
How can you prove e-infinity equals 0?
I think you mean e to the (- infinity) power. The proof would be a limit proof. The limit (as n-->infinity) of [( en) ] = 0 You should have some other limits in class that you have proven. Show that your limit is less than one of those given for all values of n then you have your proof. For instance, if you already know that lim (as n-->infinity) of [(1/n) ] = 0 then for n = 1, 1/e1 < 1/1 true for...
Asked in Math and Arithmetic
Sum of 1 plus 2 plus 3 plus 4 plus .. plus n?
n(n+1)/2 You can see this from the following: Let x=1+2+3+...+n This is the same as x=n+(n-1)+...+1 x=1+2+3+...+n x=n+(n-1)+...+1 If you add the corresponding terms on the right-hand side of the two equations together, they each equal n+1 (e.g., 1+n=n+1, 2+n-1=n+1, ..., n+1=n+1). There are n such terms. So adding the each of the left-hand sides and right-hand sides of the two equations, we get: x+x=(n+1)+(n+1)+...+(n+1) [with n (n+1) terms on the right-hand side 2x=n*(n+1) x=n*(n+1)/2 A more formal proof by induction is also possible: (1) The formula works for n=1 because...
How do you find a geometric mean?
If there are only k numbers x(1),x(2)....,x(k), the geometric mean is the kth root of the product of these k numbers. Example: find the geometric mean of 4,3,7,8 We want the fourth root of 4 x 3 x 7 x 8 = 672 =(672)^(1/4) = 5.09146 is the geometric mean. The geometric mean is normally defined only for a set of positive numbers. ...
Asked in Math and Arithmetic, Algebra, Geometry
What is the value of k when the line y kx plus 1 is a tangent to the curve y2 equals 8x?
If you mean: y = kx +1 and y^2 = 8x So if: y = kx +1 then y^2 = k^2*x^2 +2kx +1 If: y^2 = 8x then k^2*x^2 +2kx +1 = 8x Transposing terms: k^2*x^2 +2kx +1 -8x = 0 Using the discriminant: (2k -8)^2 -4*(k^2*1) = 0 Solving the discriminant: k = 2 ...
How to Derive variance of Poisson distribution?
If X has the Poisson distribution with mean l then Pr(X = k) = e-llk/k! Mean of Poisson = Sum over all k of [k*P(X = k)] which happens to be l. = Sum over all k of [k*e-llk/k!] = Sum over all k of [e-llk/(k-1)!] = Sum over all j of [le-llj/j!] where j has been substituted for k-1 = l*Sum over all j of [e-llj/j!] But the quantity being summed is simply the pdf of the Poisson distribution and so its sum over...