Draw the diagram and determine the forces.
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Draw the diagram and determine the forces. a sin 6 dN sin fdN cos fdN dN cos 0 f dN sin F. 02 A R R Rotation A SOo D....
3. If T2 = r3 cos(0) sin(d) and v2 = sin(0) cos(O)f + r sin(0)θ +...
3. If T2 = r3 cos(0) sin(d) and v2 = sin(0) cos(O)f + r sin(0)θ + r2 sin(d)φ compute the following (a) ▽T, (b) ▽.
VER, DER, 4) Prove that the rotation matrices [cos – sin 07 1(0) 4 sinŲ cos...
VER, DER, 4) Prove that the rotation matrices [cos – sin 07 1(0) 4 sinŲ cos x 0, 0 0 1 cose 0 sin 0] O(0) 4 0 1 0 , 1-sin 0 cos e ſi 0 0 1 0(0) 4 0 cos – sin 0, 0 sinº cos 0 ] are rotation matrices, that is, V-7(4) = \T(4), 6-7(0) = OT(0), $ER, 6-7(0) = $1(0), and det(\())) = 1, det(O(0)) = 1, det($(0)) = 1. Prove also that R321(4,0,0)...
Determine f(x). f′′(x)=−cos(x)+sin(x), and f(0)=1, f(π)=0. Problem. f"(t) = -cos(T) + sin(), and f(0) = 1,...
Determine f(x).
f′′(x)=−cos(x)+sin(x), and
f(0)=1, f(π)=0.
Problem. f"(t) = -cos(T) + sin(), and f(0) = 1, f(1) = 0
3. A shape is defined as: (x, y, z) = (rcos 0 sin 0,r sin sin d, r cos ø) with 0r1, T/4 < 0< 7t/4 and 0 < ¢ &l...
3. A shape is defined as: (x, y, z) = (rcos 0 sin 0,r sin sin d, r cos ø) with 0r1, T/4 < 0< 7t/4 and 0 < ¢ < T* 2 marks (a) Describe this region. an appropriate integration, determine the volume of this shape [4 marks (b) Using 3 (Continued) 3 marks (c) Parametrise the surface of this shape. 3 marks (d) Find a normal to the surface [4 marks (e) What is the surface area of...
A polar curve r = f() has parametric equations x = f(0) cos(8), y = f(0)...
A polar curve r = f() has parametric equations x = f(0) cos(8), y = f(0) sin(8). Then, dy f() cos(0) + f (0) sin(e) d/ where / --f(8) sin(0) + / (8) cos(8) do Use this formula to find the equation in rectangular coordinates of the tangent line to r = 4 cos(30) at 0 = (Use symbolic notation and fractions where needed.)
6. Find the derivative matrices for the change-of-coordinate functions, then find their determinants! (a) f(r,0)= (r co...
6. Find the derivative matrices for the change-of-coordinate functions, then find their determinants! (a) f(r,0)= (r cos 0, r sin 0) (b) f(r,0,2) (r cos 0, r sin 0, ) (c) f(p,0,)(psin o cos 9, psin o sin 0, p cos o)
6. Find the derivative matrices for the change-of-coordinate functions, then find their determinants! (a) f(r,0)= (r cos 0, r sin 0) (b) f(r,0,2) (r cos 0, r sin 0, ) (c) f(p,0,)(psin o cos 9, psin o sin...
Determine the potential for the field: } = (-6 cos (2y), 12x sin (2y), 5 cos...
Determine the potential for the field: } = (-6 cos (2y), 12x sin (2y), 5 cos (1z) – 5z sin (1x)) Do not put the constant "+c" for the potential in your answer below. f (x, y, z) = -12x*cos(2y)+5z*sin(z) Submit Answer Incorrect. Tries 1/8 Previous Tries Now calculate F. dr where C is the path † (t) = ( 4 cos t, 4 sin t, 3t) for 0 <tst. The line integral equals 0
Determine the potential for the field: } = (-6 cos (2y), 12x sin (2y), 5 cos...
Determine the potential for the field: } = (-6 cos (2y), 12x sin (2y), 5 cos (1z) – 5z sin (1z)) Do not put the constant "+c" for the potential in your answer below. f(x, y, z) = Submit Answer Tries 0/8 Now calculate 18.di where C is the path ř (t) = (4 cos t, 4 sin t, 3t) for 0 <tsa. The line integral equals
Define f: R2R3 b f(s,t) (sin(s) cos(t), sin(s) sin(t), cos(s)). (a) Describe and draw the image of f. (b) Proeve i.baat uts dilikur#xot.ial le. (c) Find the Jacobian matrix of f at (π/3, π/4) (d) Des...
Define f: R2R3 b f(s,t) (sin(s) cos(t), sin(s) sin(t), cos(s)). (a) Describe and draw the image of f. (b) Proeve i.baat uts dilikur#xot.ial le. (c) Find the Jacobian matrix of f at (π/3, π/4) (d) Describe and draw the im age of Df(m/3, π/4). (e) Draw the image of Df(n/3, π/4) translated by f(n/3, π/4). (f) Describe the relationship between the image of f and the translated image of Df(T/3,/4) in nart (e
Define f: R2R3 b f(s,t) (sin(s) cos(t),...
3. If z = f(x,y), where x = r cos, y=r sin 0 show that 222...
3. If z = f(x,y), where x = r cos, y=r sin 0 show that 222 222 1 222 1.az + + +) ar2 ду? ar2 a02 rar
3. If T2 = r3 cos(0) sin(d) and v2 = sin(0) cos(O)f + r sin(0)θ + r2 sin(d)φ compute the following (a) ▽T, (b) ▽.
VER, DER, 4) Prove that the rotation matrices [cos – sin 07 1(0) 4 sinŲ cos x 0, 0 0 1 cose 0 sin 0] O(0) 4 0 1 0 , 1-sin 0 cos e ſi 0 0 1 0(0) 4 0 cos – sin 0, 0 sinº cos 0 ] are rotation matrices, that is, V-7(4) = \T(4), 6-7(0) = OT(0), $ER, 6-7(0) = $1(0), and det(\())) = 1, det(O(0)) = 1, det($(0)) = 1. Prove also that R321(4,0,0)...
Determine f(x).
f′′(x)=−cos(x)+sin(x), and
f(0)=1, f(π)=0.
Problem. f"(t) = -cos(T) + sin(), and f(0) = 1, f(1) = 0
3. A shape is defined as: (x, y, z) = (rcos 0 sin 0,r sin sin d, r cos ø) with 0r1, T/4 < 0< 7t/4 and 0 < ¢ < T* 2 marks (a) Describe this region. an appropriate integration, determine the volume of this shape [4 marks (b) Using 3 (Continued) 3 marks (c) Parametrise the surface of this shape. 3 marks (d) Find a normal to the surface [4 marks (e) What is the surface area of...
A polar curve r = f() has parametric equations x = f(0) cos(8), y = f(0) sin(8). Then, dy f() cos(0) + f (0) sin(e) d/ where / --f(8) sin(0) + / (8) cos(8) do Use this formula to find the equation in rectangular coordinates of the tangent line to r = 4 cos(30) at 0 = (Use symbolic notation and fractions where needed.)
6. Find the derivative matrices for the change-of-coordinate functions, then find their determinants! (a) f(r,0)= (r cos 0, r sin 0) (b) f(r,0,2) (r cos 0, r sin 0, ) (c) f(p,0,)(psin o cos 9, psin o sin 0, p cos o)
6. Find the derivative matrices for the change-of-coordinate functions, then find their determinants! (a) f(r,0)= (r cos 0, r sin 0) (b) f(r,0,2) (r cos 0, r sin 0, ) (c) f(p,0,)(psin o cos 9, psin o sin...
Determine the potential for the field: } = (-6 cos (2y), 12x sin (2y), 5 cos (1z) – 5z sin (1x)) Do not put the constant "+c" for the potential in your answer below. f (x, y, z) = -12x*cos(2y)+5z*sin(z) Submit Answer Incorrect. Tries 1/8 Previous Tries Now calculate F. dr where C is the path † (t) = ( 4 cos t, 4 sin t, 3t) for 0 <tst. The line integral equals 0
Determine the potential for the field: } = (-6 cos (2y), 12x sin (2y), 5 cos (1z) – 5z sin (1z)) Do not put the constant "+c" for the potential in your answer below. f(x, y, z) = Submit Answer Tries 0/8 Now calculate 18.di where C is the path ř (t) = (4 cos t, 4 sin t, 3t) for 0 <tsa. The line integral equals
Define f: R2R3 b f(s,t) (sin(s) cos(t), sin(s) sin(t), cos(s)). (a) Describe and draw the image of f. (b) Proeve i.baat uts dilikur#xot.ial le. (c) Find the Jacobian matrix of f at (π/3, π/4) (d) Describe and draw the im age of Df(m/3, π/4). (e) Draw the image of Df(n/3, π/4) translated by f(n/3, π/4). (f) Describe the relationship between the image of f and the translated image of Df(T/3,/4) in nart (e
Define f: R2R3 b f(s,t) (sin(s) cos(t),...
3. If z = f(x,y), where x = r cos, y=r sin 0 show that 222 222 1 222 1.az + + +) ar2 ду? ar2 a02 rar
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