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consider SO(1,1) having only one free parametrer . how it would act on a vector of co-ordinate differentials dxµ=[■(cdt/dx)] where µ=0,1 .µ is in superscript.
a) construct a matrix representing the one type of transformation in this group. verify explicitly that satisfy the condition defining SO(1,1)
b) construct the dual vector dxµ . (µ in subsript)
c) seperately transform the vector and dual vector i.e determine dxµ(prime sign on µ is there), then confirm that it is invariant
a) construct a matrix representing the one type of transformation in this group. verify explicitly that satisfy the condition defining SO(1,1)
b) construct the dual vector dxµ . (µ in subsript)
c) seperately transform the vector and dual vector i.e determine dxµ(prime sign on µ is there), then confirm that it is invariant
what is 3082.24 divided by 24
If I have two apples and I eat 1 apple. How many purple space aliens exist with our universe?
Determine the metric coefficients for the coordinate system (u,v,z) whose coordinates are
related to the Cartesian coordinates by the following equations
x=1/2(u^+v^);y=2uv;z=z
Is the system orthogonal?
related to the Cartesian coordinates by the following equations
x=1/2(u^+v^);y=2uv;z=z
Is the system orthogonal?
The position vector of an object of mass m moving along a curve is given by
, 0 1
ˆ cos ˆ
sin ˆ
( )
2
r t = at i + bt j+ bt k ≤t ≤
r
, where a and b are constants. Calculate the force
acting on the object and the work done by the force
, 0 1
ˆ cos ˆ
sin ˆ
( )
2
r t = at i + bt j+ bt k ≤t ≤
r
, where a and b are constants. Calculate the force
acting on the object and the work done by the force
The measurements of the bulk modulus of a material at different temperatures is as follows:
T( ͦ C ) 20 500 1000 1200 1400 1500
K (G Pa) 203 197 191 188 186 184
Determine the regression equation for this data.
T( ͦ C ) 20 500 1000 1200 1400 1500
K (G Pa) 203 197 191 188 186 184
Determine the regression equation for this data.
Determine the value of the constant a for which the vector field
F i j k
ˆ
( 2 )
ˆ
( )
ˆ 2( )
2 2 2 2 2 2
= x y + z + xy − x z + axyz − x y
r
is incompressible
F i j k
ˆ
( 2 )
ˆ
( )
ˆ 2( )
2 2 2 2 2 2
= x y + z + xy − x z + axyz − x y
r
is incompressible
7 Determine
∫x2+1(x+2)3
ln(x+2)+4x+2−52(x+3)2+c
ln(x+2)−4x+2−52(x+3)2+c
−ln(x+2)−4x+2−52(x+3)2+c
ln(x−2)+4x−2−52(x+3)2+c
8 Find the volume of a sphere generated by a semicircle
y=(√r2−x)
revolving around the x-axis
−π−r32
4πr32
πr34
4πr33
9 Evaluate
∫x2e3x
e3x3(x2−2x3+29)+c
−e3x3(x2+2x3−29)+c
e2x3(x3−x4+29)+c
ex3(x2+2x3−25)+c
10 Given f(x) =
(7x4−5x3)
, evaluate
df(x)dx
7x4−5x3
2x3−15x2
28x2−15x2
28x3−15x2
∫x2+1(x+2)3
ln(x+2)+4x+2−52(x+3)2+c
ln(x+2)−4x+2−52(x+3)2+c
−ln(x+2)−4x+2−52(x+3)2+c
ln(x−2)+4x−2−52(x+3)2+c
8 Find the volume of a sphere generated by a semicircle
y=(√r2−x)
revolving around the x-axis
−π−r32
4πr32
πr34
4πr33
9 Evaluate
∫x2e3x
e3x3(x2−2x3+29)+c
−e3x3(x2+2x3−29)+c
e2x3(x3−x4+29)+c
ex3(x2+2x3−25)+c
10 Given f(x) =
(7x4−5x3)
, evaluate
df(x)dx
7x4−5x3
2x3−15x2
28x2−15x2
28x3−15x2
1 Evaluate
∫e4xdx
14e4x+c
ex+c
3ex3+c
13ex+c
2 Evaluate
∫xe6xdx
x6e6x−1136e6x+c
x3e6x+116e6x+c
x6e6x+1136e6x+c
−x6e6x+1136e6x+c
3 Find
∫xcosax2dx
with respect to x
cos3x+c
sin2x+c
sec2x+1
12asinax2+c
∫e4xdx
14e4x+c
ex+c
3ex3+c
13ex+c
2 Evaluate
∫xe6xdx
x6e6x−1136e6x+c
x3e6x+116e6x+c
x6e6x+1136e6x+c
−x6e6x+1136e6x+c
3 Find
∫xcosax2dx
with respect to x
cos3x+c
sin2x+c
sec2x+1
12asinax2+c
1 Evaluate
∫e4xdx
∫e4xdx
14e4x+c
14e4x+c
ex+c
ex+c
3ex3+c
3ex3+c
13ex+c
13ex+c
2 Evaluate
∫xe6xdx
∫xe6xdx
x6e6x−1136e6x+c
x6e6x−1136e6x+c
x3e6x+116e6x+c
x3e6x+116e6x+c
x6e6x+1136e6x+c
x6e6x+1136e6x+c
−x6e6x+1136e6x+c
−x6e6x+1136e6x+c
∫e4xdx
∫e4xdx
14e4x+c
14e4x+c
ex+c
ex+c
3ex3+c
3ex3+c
13ex+c
13ex+c
2 Evaluate
∫xe6xdx
∫xe6xdx
x6e6x−1136e6x+c
x6e6x−1136e6x+c
x3e6x+116e6x+c
x3e6x+116e6x+c
x6e6x+1136e6x+c
x6e6x+1136e6x+c
−x6e6x+1136e6x+c
−x6e6x+1136e6x+c
