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22 6-8kR HG SKL 104F vi $8.2K 1-sta 20uF 2i y en a) Calcula te the total AvT Of the Find low utoff freqvency b)...
te tt 9 Let S be the surface defined by r2 y-22= 1 and 0 15...
te tt 9 Let S be the surface defined by r2 y-22= 1 and 0 15 points by the normal direction toward the z-axis. Find the flux of the velocity field V 1and oriented (z2-ry2)i+(2.2y -yz2)j+ (y2z- 2r2)k across S Solution. To use Gauss Theorem, define C and C2 such that C1 {(a, y, z ) | a + y? < 2, z = 1} C2={(r,y,)| +y1.0} 11 TALK X W P S ww F6 & # 2 3 4...
with clear writing please QUESTION 1 (Total 15 marks) VECTORS If A -2i+2k and B -3...
with clear writing please
QUESTION 1 (Total 15 marks) VECTORS If A -2i+2k and B -3 i+ 3j +3k find: (a) the magnitude of B A B Ax B ii. iIl (b) If i, j, k are the unit vectors of the x, y, and z axes, evaluate: jx k iV. ix i
Exercise 6. (4pts each, 20pts total) Given the complex number zg = -1 + 2i, find...
Exercise 6. (4pts each, 20pts total) Given the complex number zg = -1 + 2i, find m distinct m-th roots (z/m) for the following values of m. You may leave your answer in exponential form. (i) m = 2 (ii) m=4 (iii) m = 10 (iv) m= 45 (v) m = 100
6. Find the dy/dt for each of the following: a) y = e2t+4 b) y =...
6. Find the dy/dt for each of the following: a) y = e2t+4 b) y = te c) y = t?e21 d) y = log(77) e) y = log(7t(1 -t) 1
Erasel 6 1 - + y Draw 2. Mechanisms: (10 points each, 60 points total) a....
Erasel 6 1 - + y Draw 2. Mechanisms: (10 points each, 60 points total) a. OH CH,OH (just solvent) Br b. CI dos CH,CH,OH EXOCACHE te H2SO4 OH d. Br Br2 CH3OH "OCHE CHAN heat 1. Hg(OA) CH, OH 2. NaBH OCH Type here to search Short Answer 1. How would you synthesize the following compound starting from the compounds provided? (10 points) Ph Starting from Br We Br Ph
22 If f(L,y) = 561, for 0 <<<y<1. find o elsewhere, (a) f(y) (b) f(z|y) (c)...
22 If f(L,y) = 561, for 0 <<<y<1. find o elsewhere, (a) f(y) (b) f(z|y) (c) E[X | Y = y) (d) EX | Y = 0.5]
EXAMPLE 1 (a) Find the derivative of r(t) = (3 + t4)1+ te-y + sin(40k. (b) Find the unit tangent vector at the point t0...
EXAMPLE 1 (a) Find the derivative of r(t) = (3 + t4)1+ te-y + sin(40k. (b) Find the unit tangent vector at the point t0. SOLUTION (a) According to this theorem, we differentiate each component of r: t 45 cos (4t) r(t) + 3 (b) Since r(0)= and r(o) j+4k, the unit tangent vector at the point (3, 0, 0) is i+ 4k T(0) = L'(0)--
EXAMPLE 1 (a) Find the derivative of r(t) = (3 + t4)1+ te-y +...
(6 points) Let X and Y be independent random variables with p.d.f.s fx(x) -{ { 1-22...
(6 points) Let X and Y be independent random variables with p.d.f.s fx(x) -{ { 1-22 0, for |2|<1, otherwise. fy(y) = for y>0, otherwise. 0, Let W = XY (a) (2 points) Find the p.d.f. of W, fw(w). (b) (2 points) Find the moment generating function of W2, Mw?(t) = E (e«w?). (c) (2 points) Find the conditional expectation of W given Y = y, E(W|Y = y).
Find parameterisations x(t), y(t), t є 1 (a) (b) (c) for each of the following curves: 2. The straight line from 4+2i to 3+5i; The circle of radius 2 centered at 3-i oriented counter-clockwise; The g...
Find parameterisations x(t), y(t), t є 1 (a) (b) (c) for each of the following curves: 2. The straight line from 4+2i to 3+5i; The circle of radius 2 centered at 3-i oriented counter-clockwise; The graph of the cosine function over the interval [π/4,2n
Find parameterisations x(t), y(t), t є 1 (a) (b) (c) for each of the following curves: 2. The straight line from 4+2i to 3+5i; The circle of radius 2 centered at 3-i oriented counter-clockwise; The graph...
question #6 1. Sketch the following surfaces: (a) z-+y2/9 (b) a2 =y2 +22 (c) 2/4+(y-1)2+(z+1)/9 1...
question #6
1. Sketch the following surfaces: (a) z-+y2/9 (b) a2 =y2 +22 (c) 2/4+(y-1)2+(z+1)/9 1 (d) r2+y-22+1 0 (e) -y2+-1 0. 2. Find an equation for the surface consisting of all points that are- point (1,-3, 5) and the plane r = 3. 3. Sketch the curve F(t)<t cos(t), t sin (t), t > 4. Find a vector equation that represents the curve of the intersec r2y =9 and the plane y + z = 2. 5. Find a...
te tt 9 Let S be the surface defined by r2 y-22= 1 and 0 15 points by the normal direction toward the z-axis. Find the flux of the velocity field V 1and oriented (z2-ry2)i+(2.2y -yz2)j+ (y2z- 2r2)k across S Solution. To use Gauss Theorem, define C and C2 such that C1 {(a, y, z ) | a + y? < 2, z = 1} C2={(r,y,)| +y1.0} 11 TALK X W P S ww F6 & # 2 3 4...
with clear writing please
QUESTION 1 (Total 15 marks) VECTORS If A -2i+2k and B -3 i+ 3j +3k find: (a) the magnitude of B A B Ax B ii. iIl (b) If i, j, k are the unit vectors of the x, y, and z axes, evaluate: jx k iV. ix i
Exercise 6. (4pts each, 20pts total) Given the complex number zg = -1 + 2i, find m distinct m-th roots (z/m) for the following values of m. You may leave your answer in exponential form. (i) m = 2 (ii) m=4 (iii) m = 10 (iv) m= 45 (v) m = 100
6. Find the dy/dt for each of the following: a) y = e2t+4 b) y = te c) y = t?e21 d) y = log(77) e) y = log(7t(1 -t) 1
Erasel 6 1 - + y Draw 2. Mechanisms: (10 points each, 60 points total) a. OH CH,OH (just solvent) Br b. CI dos CH,CH,OH EXOCACHE te H2SO4 OH d. Br Br2 CH3OH "OCHE CHAN heat 1. Hg(OA) CH, OH 2. NaBH OCH Type here to search Short Answer 1. How would you synthesize the following compound starting from the compounds provided? (10 points) Ph Starting from Br We Br Ph
22 If f(L,y) = 561, for 0 <<<y<1. find o elsewhere, (a) f(y) (b) f(z|y) (c) E[X | Y = y) (d) EX | Y = 0.5]
EXAMPLE 1 (a) Find the derivative of r(t) = (3 + t4)1+ te-y + sin(40k. (b) Find the unit tangent vector at the point t0. SOLUTION (a) According to this theorem, we differentiate each component of r: t 45 cos (4t) r(t) + 3 (b) Since r(0)= and r(o) j+4k, the unit tangent vector at the point (3, 0, 0) is i+ 4k T(0) = L'(0)--
EXAMPLE 1 (a) Find the derivative of r(t) = (3 + t4)1+ te-y +...
(6 points) Let X and Y be independent random variables with p.d.f.s fx(x) -{ { 1-22 0, for |2|<1, otherwise. fy(y) = for y>0, otherwise. 0, Let W = XY (a) (2 points) Find the p.d.f. of W, fw(w). (b) (2 points) Find the moment generating function of W2, Mw?(t) = E (e«w?). (c) (2 points) Find the conditional expectation of W given Y = y, E(W|Y = y).
Find parameterisations x(t), y(t), t є 1 (a) (b) (c) for each of the following curves: 2. The straight line from 4+2i to 3+5i; The circle of radius 2 centered at 3-i oriented counter-clockwise; The graph of the cosine function over the interval [π/4,2n
Find parameterisations x(t), y(t), t є 1 (a) (b) (c) for each of the following curves: 2. The straight line from 4+2i to 3+5i; The circle of radius 2 centered at 3-i oriented counter-clockwise; The graph...
question #6
1. Sketch the following surfaces: (a) z-+y2/9 (b) a2 =y2 +22 (c) 2/4+(y-1)2+(z+1)/9 1 (d) r2+y-22+1 0 (e) -y2+-1 0. 2. Find an equation for the surface consisting of all points that are- point (1,-3, 5) and the plane r = 3. 3. Sketch the curve F(t)<t cos(t), t sin (t), t > 4. Find a vector equation that represents the curve of the intersec r2y =9 and the plane y + z = 2. 5. Find a...
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