2) For a spherical charge distribution in the air: po (02 – r2), when r <a p. when r>a lo, (a) Find E and for r>a (b) Find E and for r<a (c) Find the total charge (d) Show that E is maximum when r=0.7454a
JJ JR 3. Let R be the first-quadrant region bounded by the circles a2 y 4r, 2y10z and the 6y. Use the transformation -2y, 2 y circles a2 +y and r2 + y r2 + y deimegal ll.rdpdrdy to evaluate the i
JJ JR 3. Let R be the first-quadrant region bounded by the circles a2 y 4r, 2y10z and the 6y. Use the transformation -2y, 2 y circles a2 +y and r2 + y r2 + y deimegal ll.rdpdrdy...
(a) Let R be a commutative ring. Given a finite subset {ai, a2, , an} of R, con- sider the set {rial + r202 + . . . + rnan I ri, r2, . . . , rn є R), which we denote by 〈a1, a2 , . . . , Prove that 〈a1, a2, . . . , an〉 įs an ideal of R. (If an ideal 1 = 〈a1, аг, . . . , an) for some a,...
Consider the following tables R1 and R2: R1.A1 R1.B1 ------------ 1 1 NULL 2 3 NULL R2.A2 R2.B2 ------------ 1 1 NULL 2 3 NULL The tuple (3, NULL, 3, NULL) appears in the answer of which of the following SQL Statements? Check all that apply A. select * from R1,R2; B. select * from R1,R2 where R1.A1=R2.A2; C. select * from R1,R2 where R1.A1=R2.A2 and R1.B1=R2.B2; Suppose relation R(A,B,C) has the following tuples A B C ----- 2 3 4 5 3 4...
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3 (10) Let = Re', z = re (0<r< R) be two complex numbers. Show the following identities hold: R2 2 OO = Re = 1 +2 C-z ΣΑ. R2 - 2rR cos (-0)r2 coS n(-e) n=1
Question 3. Use the class equation to show that, if G is a group of order p' for p a prime and r > 1 (such a G is called a p-group), then Z(G) must be nontrivial
Question 3 - 15 mai You should be able to answer this question after studying Unit 7. (a) Find the partial fraction expansion of the rational expression 2a3- 3a2 - 18x 17 a2 -3r- 4 10 (b) Use the partfrac command in Maxima to verify your answer to part (a). Include a screenshot or printout of your Maxima worksheet in your answer (c) Hence (without using Maxima) find the integral 2r332 -18x +17 [4
Question 3 - 15 mai You...
3. Show tha the system of equations where r r2 + y2 has a limit cycle at r - To for each ro such that F(ro) = 0 and F,(m)メ0. The orbit is called asymptotically orbitally stable if F(ro) >0 and unstable if F(ro)0. For the case when F(r)r2)(2- 4r 3) find all limit cycles, determine the orbital stability, and sketch the orbits in the phase plane.
3. Show tha the system of equations where r r2 + y2 has...
JJ JR 3. Let R be the first-quadrant region bounded by the circles a2 y 4r, 2y10z and the 6y. Use the transformation -2y, 2 y circles a2 +y and r2 + y r2 + y deimegal ll.rdpdrdy to evaluate the i
2. Let 6 marks (a) Find f(x),f"(x), and f"(x). (b) Find the second order Taylor expansion of f at 1, namely f(r) = ao + ala-1 ) + a2(z-1)2 + R2(x), where Ra is the remainder. You should find ao, a, a2, and R(p). 8 marks that the error in this estimation (i.e., R2(0.9)1) is at most 10-3. 6 marks (c) Use the Taylor expansion found above to estimate the value of f(0.9). Show Find f(x), f"(), and f" (b)...