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Given that
ϕ
=
l
n
|
r
|
ϕ=ln|r|
such that r=xi+yj+zk find
▽
ϕ
ϕ
=
l
n
|
r
|
ϕ=ln|r|
such that r=xi+yj+zk find
▽
ϕ
Determine the directional derivative of
f
=
x
y
2
+
y
z
3
f=xy2+yz3
at the point (2, -1, 1) in the direction of vector i+2j+2k
f
=
x
y
2
+
y
z
3
f=xy2+yz3
at the point (2, -1, 1) in the direction of vector i+2j+2k
Find the curl of
A
=
x
2
y
i
−
2
x
z
j
+
2
y
z
k
A=x2yi−2xzj+2yzk
at the point (1, 0, 2).
A
=
x
2
y
i
−
2
x
z
j
+
2
y
z
k
A=x2yi−2xzj+2yzk
at the point (1, 0, 2).
Math
Determine the constant b such that
A
=
(
b
x
+
4
y
2
z
)
i
+
(
x
3
s
i
n
z
−
3
y
)
j
–
(
e
x
+
4
c
o
s
x
2
y
)
k
A=(bx+4y2z)i+(x3sinz−3y)j–(ex+4cosx2y)k
is a solenoidal
A
=
(
b
x
+
4
y
2
z
)
i
+
(
x
3
s
i
n
z
−
3
y
)
j
–
(
e
x
+
4
c
o
s
x
2
y
)
k
A=(bx+4y2z)i+(x3sinz−3y)j–(ex+4cosx2y)k
is a solenoidal
Math
Find the unit outward drawn normal to the surface
(
x
−
1
)
2
+
y
2
+
(
z
+
2
)
2
(x−1)2+y2+(z+2)2
= 9 at the point (3, 1, -4)
(
x
−
1
)
2
+
y
2
+
(
z
+
2
)
2
(x−1)2+y2+(z+2)2
= 9 at the point (3, 1, -4)
Math
If
f
=
x
2
y
z
f=x2yz
and
g
=
x
y
−
3
z
2
g=xy−3z2
, calculate $$ \triangledown\cdot (\triangledown f x \triangledown g)
f
=
x
2
y
z
f=x2yz
and
g
=
x
y
−
3
z
2
g=xy−3z2
, calculate $$ \triangledown\cdot (\triangledown f x \triangledown g)
Math
Determine the constants a and b such that the curl of
(
2
x
y
+
3
y
z
)
i
+
(
x
2
+
a
x
z
–
4
z
2
)
j
+
(
3
x
y
+
2
b
y
z
)
k
=
0
(
2
x
y
+
3
y
z
)
i
+
(
x
2
+
a
x
z
–
4
z
2
)
j
+
(
3
x
y
+
2
b
y
z
)
k
=
0
what is the answer to y=-x+5
Math
A = Sin^-1 Root 3/2 + Sin^-1 1/3
B = Cos^-1 Root 3/2 + Cos^-1 1/3
Show That B > A
B = Cos^-1 Root 3/2 + Cos^-1 1/3
Show That B > A
Arthur is hired to road test a hybrid car for 3 months. He drives the car an average of 85 miles a day for 91 days. How many miles did Arthur drive the car?
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#340153 on Dec 2023
#340153 on Dec 2023