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1. ### The digits N,V,K,J,C,L,M,Y are all distinct. Evaluate V.?

...that C = 2 and Y = 5. In summary, M = 0 L = 1 C = 2 K = 3 Y = 5 J = 7 V = 8 N = 9 The equation...

1 Answers · Science & Mathematics · 06/05/2010

2. ### What is the value of k + c if f(x) is everywhere differentiable. ?

...28 + c c = 6k - 10 12k = 28 + 6k - 10 6k = 18 k = 3 c = 6(3) - 10 c = 8 k + c = 3 + 8 = 11

1 Answers · Science & Mathematics · 11/01/2009

3. ### ∑{k=1,n} [(-1)^k·( n C k) ]?

Use the Binomial Theorem: (1 + x)^n = ∑(k = 0 to n) C(n, k) x^k. Let x = -1: 0 = ∑(k = 0 to n) C(n, k) (-1)^k...

1 Answers · Science & Mathematics · 05/02/2014

4. ### Prove discrete math identity C(n,r)⋅C(r,k) = C(n,k)⋅C(n-k,r-k)?

... X. This corresponds to the product C(n,k)⋅C(n-k,r-k). Every such pair of subsets A,B is...

4 Answers · Science & Mathematics · 27/07/2013

5. ### ∑k(k-1)C(n,k) using the binomial theorem and some calculus, evaluate?

By the Binomial Theorem, (1 + x)^n = sum(k=0 to n) C(n,k) x^k. Differentiating both sides twice, we get n(n - 1) (1 + x...

1 Answers · Science & Mathematics · 19/10/2009

6. ### An equation of the form y = k/(x^2 +bx +c) has a graph that matches the one shown. Find the equation.?

-3/8 = k / c -3c = 8k c = -8k/3 k / (1 + b - 8k/3) = undefined 1 + b - 8k...4b = 8k/3 - 48/3 b = (2k - 12) / 3 8k + 3 = 2k - 12 6k = -15 k = -2.5 b = (-5 - 12)/3 b = -17/3 c = -8k / 3 c = 20/3 y = -2.5 / (x^2 - 17x/3 + 20/3) y = -7...

1 Answers · Science & Mathematics · 08/11/2009

7. ### Algebra 2 question. Find k:?

Solving for k from x/k - c/w = y add c/w to both sides x/k = y + c/w x/k = (wy+c)/w cross multiply k(wy+c) = wx divide both sides by (wy+c) k = wx/(wy+c)

1 Answers · Science & Mathematics · 23/01/2013

8. ### Given 3 points, find a, b, c, h, k?

...respectively. Reference (2) gives formulas for h=-b/2a and k=c - [(b^2)[(4a)]. Using these we answer the questions that h = -(-12)/[2...

1 Answers · Science & Mathematics · 21/02/2013

9. ### How can I eliminate constants k and c without using a number?

Notice that y = k(x - a)^2 + c has its vertex at x = a, so the point (a, b) is the parabola...0) lies on the parabola, so plugging in x = y = 0 yields: 0 = k(0 - a)^2 + b = ka^2 + b ==> k = -b/a^2. Thus, the equation of the parabola...

1 Answers · Science & Mathematics · 22/11/2012

10. ### If a, b and c are relatively prime to each other then there exists k such that a + k = b + k (mod c). Why?

This has to be mis-stated. k (mod c) is a constant, so if a + k = b + k (mod c) then we can subtract k from both...

1 Answers · Science & Mathematics · 27/06/2012