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1. ### Show that p_k = p_(k-1) + (3k-2) for k >=2. Conclude that p_n = sum from k=1 to n of (3k-2).?

Let k ≥ 2. Then p_(k - 1) + 3k - 2 = (k - 1)[3(k - 1) - 1]/2 + (6k - 4)/2 = [(k - 1)(3k - 3 - 1) + 6k - 4]/2 = [(k - 1)(3k - 4) + 6k - 4]/2 = (3k² - 7k...

1 Answers · Science & Mathematics · 13/09/2009

2. ### How do you solve k * 3^k = 1,000,000,000 algebraically/on paper?

k * 3^k = 1,000,000,000 Start by taking the natural logarithm of both sides of the equation to remove that variable from the exponent:*** ln(3^k)(k) = ln(1,000,000,000) Now the exponent of a factor here can be ...

1 Answers · Science & Mathematics · 21/09/2008

3. ### Solving Polynomial Equations k(k-5)>0?

k(k - 5) > 0 in two cases: 1) k > 0 and (k - 5) > 0 2) k < 0 and (k - 5) < 0 In case 1, k > 0 and k > 5; both of these are true when k > 5. In case 2, k...

1 Answers · Science & Mathematics · 11/04/2010

4. ### Find k such that the equation kx^2+x+64k=0?

k=(-x)/(x^2+64)

1 Answers · Science & Mathematics · 09/10/2007

5. ### Solve -7k + 5 + k = 47 k =?

-7k + 5 + k = 47 -6k=47-5 k=42/(-6) k=-7

2 Answers · Science & Mathematics · 06/11/2011

6. ### Simplify the following factorial:(2k+1)!/(2)(k!)?

(2k+1) * (2k) * (2k-1) * ... * (k+2) * (k+1) / 2 = (2k+1) * k * [(2k-1) * ... * (k+2) * (k+1)] In...ellipsis notation from becoming ambiguous. (Otherwise the k factor is out of sequence and makes that notation unclear.)

1 Answers · Science & Mathematics · 18/07/2011

7. ### How can the answer also be 3 > k if k > 3? (quadratics)?

(k - 1)x² - (k + 1)x + 2 = 0 first off, notice that k <> 1 because... linear and can have only 1 solution now, proceed as you did until: (k - 3)² > 0 k > 0 ← this step is not justified...

1 Answers · Science & Mathematics · 02/04/2011

8. ### Calculate the derivative of k?

derivative of k(x)=20(2x+5)^8*(4x+1) TO THE SMART GUY THAT... A "BAD ANSWER" Using the chain rule: k'(x)=4(5+2x)^9 + 4x*9(5+2x)^8 *2 =4(5+2x)^9 + 72x(5+2x)^8 Putting...

5 Answers · Science & Mathematics · 12/03/2007

9. ### How do you solve for K?

K-9/27 =7/9 Step 1, Multiply 27 to the whole entire problem. 27(K-9/27 =7/9) 27K - 9 = 21 Step 2, Add 9 and Divide...

2 Answers · Science & Mathematics · 05/05/2012

10. ### how do you find the integral from 0 to k?

k ∫ (2kx - x^2)dx = 18 0 ....................k (kx^2 - x^3/3) | = 18 ....................0 k(k^2) - k^3/3 - (k(0^2) - 0^3/3) = 18...

1 Answers · Science & Mathematics · 02/05/2011