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A 1. Let 2n (equally spaced) points ways to join these points in pairs intersect, equals the nth Catalan number C on a...
Ten points P1, P2,...,P10 are equally spaced around a circle. They are connected in separate pairs by 5 line segments. How many ways can such line segments be drawn so that only one pair of line segments intersect?
3. (4 points) Let Nm(G) be the the number of ways to properly color the vertices of a graph G with m colors. Pn and Cn are the path and circuit (or cycle) Show that on n vertices, respectively. Nm(P N(C= (m - 1) (-1)"-1 (m 1)"-2)
3. (4 points) Let Nm(G) be the the number of ways to properly color the vertices of a graph G with m colors. Pn and Cn are the path and circuit (or cycle)...
1/2 points Three balls, with charges of +4q, -2q, and -q, are equally spaced along a line. The spacing between different ways, as shown in the figure. In each case, the balls are in an isolated region of space very far from anything eise. 2 (a) Rank the three cases, from largest to smallest, based on the magnitude of the net force experienced by the ball with the +4q charge. (Use only "or"symbols. Do not include any parentheses around the...
Need help with A-C
HWP 06.03: A "parabolically oscillating voltage of half-period T" is defined by: o)-A(2) V(t) = A if t falls into the so-called "nth period interval", defined by: where n is an integer Note that for any given time t, there is always exactly only one integer n so that t falls into the nth period interval. The nth period intervals cover the entire real t-axis contiguously and without overlap, for n - 0,1, 2, +3 (a)...
I ONLY NEED B AND C
HWP 06.03: A "parabolically oscillating voltage of half-period T" is defined by: o)-A(2) V(t) = A if t falls into the so-called "nth period interval", defined by: where n is an integer Note that for any given time t, there is always exactly only one integer n so that t falls into the nth period interval. The nth period intervals cover the entire real t-axis contiguously and without overlap, for n - 0,1, 2,...
1. (10 points) Write an efficient iterative (i.e., loop-based) function Fibonnaci(n) that returns the nth Fibonnaci number. By definition Fibonnaci(0) is 1, Fibonnaci(1) is 1, Fibonnaci(2) is 2, Fibonnaci(3) is 3, Fibonnaci(4) is 5, and so on. Your function may only use a constant amount of memory (i.e. no auxiliary array). Argue that the running time of the function is Θ(n), i.e. the function is linear in n. 2. (10 points) Order the following functions by growth rate: N, \N,...
Problem 1: Let W(n) be the number of times "whatsup" is printed by Algorithm WHATSUP (see below) on input n. Determine the asymptotic value of W(n). Algorithm WHATSUP (n: integer) fori1 to 2n do for j 1 to (i+1)2 do print("whatsup") Your solution must consist of the following steps: (a) First express W(n) using summation notation Σ (b) Next, give a closed-form formula for W(n). (A "closed-form formula" should be a simple arithmetio expression without any summation symbols.) (c) Finally,...
→ (1 point) Let Vf-6xe-r sin(5y) +1 5e* cos(Sy) j. Find the change inf between (0,0) and (1, n/2) in two ways. (a) First, find the change by computing the line integral c Vf di, where C is a curve connecting (0,0) and (1, π/2) The simplest curve is the line segment joining these points. Parameterize it: with 0 t 1, K) = dt Note that this isn't a very pleasant integral to evaluate by hand (though we could easily...
do the problem no 1
Let r, r2 Tm be a given set of positive rational numbers whose sum is 1. Define the function f by f(n) = n - nfor each positive integer n. Determine the minimum and maximum values of f(n) k=1 An acute angle XCY and points A and B on the rays CX and CY, respectively, are given such that |CX| < \CA = |CB| < \CY]. Show how to construct a line meeting the ray...