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1. ### Consider a complete graph with n vertices, and a random walker?

... that when the walker moves from a vertex , k vertices out of n-1 vertices are non...2u + 3u^2 + ...] = (1-u)[1/(1-u)^2] ← see (note) = 1/(1-u) = 1/[k/(n-1)] = (n-1)/k And k changes from n-1 to...

1 Answers · Science & Mathematics · 06/06/2019

2. ### which of the following values does the series sigma of k=0 to infinity of 1/((4^k)k!) represent?

https://www.wolframalpha.com/input/?i=sum(1%2F(4%5E(k)+*+k!)+,+k+%3D+0+,+k+%3D+infinity) e^(1/4)

2 Answers · Science & Mathematics · 07/06/2019

3. ### Write the equation of an ellipse centered at the origin with foci at (0, -3) and (0, 3) and a major axis of 10.?

...so the ellipse is vertical. General equation for a vertical ellipse:  (y-k)²/a² + (x-h)²/b² = 1 with  a² ≥ b²...

4 Answers · Science & Mathematics · 29/05/2019

4. ### Hey People, I need help with some math questions on Parabolas, 11)What is the equation of a parabola with vertex (0, 0) and directrix y = 12?

... equation for a down-opening parabola:  y = a(x-h)² + k with  a<0  vertex (h,k)  focal length p = 1/|4a|  focus (h,k-p...

2 Answers · Science & Mathematics · 29/05/2019

5. ### Find an equation of an osculating circle to the curve?

...gt; The cross product r(t)’Xr(t)’’ at t = 0 is: | i. j. k| |-1 1 0| | 2 2 0| = -4k ||r’(t) X r’’(t)|| = 4 From equation 1...

3 Answers · Science & Mathematics · 30/05/2019

6. ### 2 d^2 X/dt^2 + 5 dx/dt + 2x = 5 sin t ?

...39; + 2X = 0, assume X = e^(kt), you get 2k^2 + 5k + 2 = 0 => (2k + 1)(k + 2) = 0 => k = -1/2 or -2. So X_h = Ae^(-1/2 t) + Be...

2 Answers · Science & Mathematics · 26/05/2019

7. ### what is the probability of getting exactly 1 five if you roll a fair die 10 times?

...the other 9 rolls were 5. In general, the probability of exactly k of n independent trials have a particular result, with probability p for that result...

3 Answers · Science & Mathematics · 26/05/2019

8. ### If point A, having coordinates (p,3) and point B, with coordinates (6,p) lie on the line having a slope of 2, what is the value of p?

Relationship between abscissas: p + k = 6 Relationship between ordinates: 3 + 2k = p for some real value of k (that we now cancel out via substitution) 3 + 2(6 - p) = p 15 = 3p p = 5

8 Answers · Science & Mathematics · 23/05/2019

9. ### What are the vertices, covertices, and foci of the ellipse (x-5)^2/64 + (y-10)^2/100 = 1?

...so the ellipse is vertical. General equation for a vertical ellipse:  (y-k)²/a² + (x-h)²/b² = 1 with  a ≥ b  center (h,k...

4 Answers · Science & Mathematics · 21/05/2019

10. ### 2sin^2 theta- 9sin theta=5?

sin(t) = x 2x^2 - 9x = 5 2x^2 - 9x - 5 = 0 x = (9 +/- sqrt(81 + 40)) / 4 x = (9 +/- 11) / 4 x = 20/4 , -2/4 x = 5 , -1/2 sin(t) = 5 , -1/2 sin(t) = 5 has no solution sin(t) = -1/2 t = 210 + 360 * k , 330 + 360 * k k is an integer

1 Answers · Science & Mathematics · 22/05/2019