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If
A=5t2+tj−t3k
A=5t2+tj−t3k
and
B=sinti−costj
B=sin⁡ti−cos⁡tj

. evaluate
ddt(A⋅B)

If
A=5t2+tj−t3k
A=5t2+tj−t3k
and
B=sinti−costj
B=sin⁡ti−cos⁡tj

. evaluate
ddt(A×B)

If
A=5t2+tj−t3k
A=5t2+tj−t3k
and
B=sinti−costj
B=sin⁡ti−cos⁡tj

. evaluate
ddt(A⋅A)

If
A=sinui+cosuj+uk
A=sin⁡ui+cos⁡uj+uk
,
B=cosui−sinuj−3k
B=cosui−sinuj−3k
and
C=2i+3j−k
C=2i+3j−k

, evaluate
ddu(A×(B×C))
ddu(A×(B×C))
at u=0

Let
A=x2yzi−2xz3j−xz2
A=x2yzi−2xz3j−xz2
and
B=4zi+yj+4x2k
B=4zi+yj+4x2k

, find
∂2∂x∂y(A×B)
∂2∂x∂y(A×B)
at (1,0,-2)

solve
d2Adt2−4dAdt−5A=0
Show that if R is a partial ordering on a set A, then there exists a linear ordering R* on A such that R ⊆ R*
Assume that whenever C is a subset of A for which <' is a linear ordering on C, then C has an upper bound in A, and assume that < is a partial ordering on A. Using these assumptions, prove the well ordering theorem that says: for any set A, there is a well ordering on A.
1. Simplify(√ 3 – 1)3
2. Simplify 4(2n+1 )- 2n+2
--------------------
2n+1 - 2n

3. Given that log2 x + log381 = 1
4. Factorize 6x2 - xy - y2 - 2 x+ y
5. Given that P1(x) = 2x2 + 4x2- x+1
Ramona completed a homework assignment consisting of 30 questions. If 3/10 of her work was incorrect, home many questions did Ramona answer correctly
6 tractors take 11 days to collect the harvest. How long would it take 18 tractors to do the same amount of work?
the traffic lights at three different road crossing change after every 48 seconds, 72 seconds and 108 seconds respectively. if the change simultaneously at 7 a.m., at what time will they change simultaneously again?
maximize the utility function u=x1+x2 subject to y=p1x1+p2x2 also find out demand function.
6 Solve for x and y: 3x + 4y = 9, 2x + 3y =8
x = 7.5, y = - 4. 5
x = 7.0, y = - 4. 5
x = 4.5, y = - 7. 5
x = 7.5, y = - 4. 1

7 If A.x=,where A=[Math Processing Error],determine the eigen values of the matrix A, and an eigen vector corresponding to each eigen value. If [Math Processing Error],what is b
{0,1,0}
{3,0,2}
{2,0,1}
{0,1,1}

8 If A.x=[Math Processing Error],where A=[Math Processing Error],determine the eigen values of the matrix A, and an eigen vector corresponding to each eigen value. If [Math Processing Error],what is c
{2,3,0}
{-2,1,1}
{2,1,1}
{3,2,6}

9 Solve the set of linear equations by the matrix method : a+3b+2c=3 , 2a-b-3c= -8, 5a+2b+c=9. Sove for c
2
1
5
7

10 If A.x=[Math Processing Error],where A=[Math Processing Error],determine the eigen values of the matrix A, and an eigen vector corresponding to each eigen value. If [Math Processing Error],what is a
{-2,1,0}
{3,5,2}
{1,0,0}
{2,1,4}
Consider n>= 2 points in space. Prove that we can construct n-1 mutually parallel planes so that any two of the points are separated by a plane.