what is the area 1 and area 2 for that shape
Sphere 1 has surface area Ai and volume Vi and sphere 2 has surface area A2 and volume V2. If the radius of sphere 2 is 1.84 times the radius of sphere 1, what is the ratio of the areas A2/A1? Tries 0/8 What is the ratio of the volumes V2/V1? Tries 0/8 Submit Answer Submit An Post Discussion Sen
1: We define the Vandermonde Determinant, denoted V(ai,a2,... ,an), as ai a...a-1 1 2 i a2 az...a-1 al,a2 ,an ) 2. 1 an a an ...an-1 We will guide you through a proof by Mathematical Induction to show that V(a,aan) aj -ai f: Show that if we perform k Type 3 ccolumn operations by adding a multiple B, of col- umn i, where1,2,. ,k, to the last column, then the Vandermonde determinant of size (k 1) x (k 1) can...
13. Consider the sequence of numbers ao, ai, a2, a3, given by ao-2, ai-3, and for any positive integer k 2, a3ak 2ak-1. (a) Evaluate a2,a3, a4,as. Show your work. (b) Prove that for all positive integers n, an 2 +1
A cylindrical can with an open end, A2, is shown below. For area A1, T1 = 1000K and ei = 0.40. Area Az is black with T3 = 500K. Area A2 is the open top of the can. It is open to a large room whose walls are at 300K. (a) Draw the thermal circuit for this problem and label all the resistances, nodes and heat flows. (b) Find F13 and ai CA21T Аз | H-20 сут - - P=1...
5. Let p be a prime with p Ξ 1 (mod 4). Suppose that ai, a2, . . . ,a(p-1)/2 are the quadratic residues of p that lie between 1 and p - 1. Prove that 1,0 (P-1)/2 i- 1 Hint: If a is a quadratic residue less than or equal to (p-1)/2 then what is p - ai? 5. Let p be a prime with p Ξ 1 (mod 4). Suppose that ai, a2, . . . ,a(p-1)/2 are...
1) Consider the switching networks shown in Fig. 1. Let Ai, A2, and As denote the events that the switches s1, s2, and s3 are closed, respectively. Let Aab denote the event that there is a closed path between terminals a and b. Express Aab in terms of Ai, A2, and A3 for each of the networks shown. 2 Figure 1
Determine the surface area and volume of the shape shown. Each small cube is 2 cm x 2 cm x 2 cm. There are no hidden indentations. Answer the prompts. a.) Surface Area b.) Describe your surface area strategy. c.) Volume d.) Describe your volume strategy.
9. (a) Let Ao(x) = / (1-t*)dt, Ai(z) = / (1-t2) dt, and A2(z) = / (1-t2)dt. Compute these explicitly in terms ofェusing Part 2 of the Fundamental Theorem of Calculus. b) Over the interval [0,2], use your answers in part (a) to sketch the graphs of y Ao(x), y A1(x), and y A2(x) on the same set of axes. (c) How are the three graphs in part (a) related to each other? In particular, what does Part 1 of...
pigeonhole 1. Show that in every sequence (ai,a2, a100) of the letters A,B,C,D, there are two indices 1i< j < 98 such that (ai, ai+1,aj+2) = (aj, aj+1, aj+2).
15] Dynamic Programming a. We are given a set of matrices Ao.A1, A2.. An-1. which we must multiply in this order. We let (di, di+1) be the dimension of matrix Ai. The minimal number Nuj of operations required to multiply matrices (Ai,Ai+ Aj) is defined by: Explain this formula. 15] Dynamic Programming a. We are given a set of matrices Ao.A1, A2.. An-1. which we must multiply in this order. We let (di, di+1) be the dimension of matrix Ai....