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Given that A = 2i + 3j - k, B = i - j +2k and C = 3i + 4j + k find:
a) A+2B
b) |A- B+2C|
c) D such that A - B + C 3D = 0
Evaluate the following limits,if they exist,where [x] is the greatest interger function
a)lim [2x]/x as x approaches 0
b)lim x[1/x] as x approaches 0
If u=x(1-y) and v=xy, then find the value of the Jacobian ∂u,v∂(x,y)
Select one:
A -x
B x2
C -x2
D x
Find the angle nearest to the whole number between the surfaces x2+y2+z2=9 and z=x2+y2-3 at the point (2, -1, 2).
Select one:
A 560
B 550
C 54o
D 53o
In a large region, there are 450 farmers. 250 pounds of farm beetroot, 110 pounds of farm yams, 75 pounds of farm radish, 45 pounds of farm beetroot and radish, 40 pounds of farm yams and radish, and 30 pounds of farm beetroot and yams Let B, Y, and R represent the farms that grow beets, yams, and radish, respectively.
Determine the number of farmers that farm beetroot, yams, and radish.
if A=2i+j+k, B=i-2j+2k and C=3i-4j+2k , find the projection A+C in the direction of B.
Round the answer to this question to the nearest rand. David borrowed R911012,00
R911012,00 to refurbish his holiday home. The loan requires monthly repayments over 12 years. When he borrowed the money, the interest rate was 12,4% per annum, compounded monthly, but five years later the bank increased the annual interest rate to 13,9%, in line with market rates. After five years the present value of the loan is R682081,77
R682081,77. With the new interest rate, his monthly payments will increase by
Find out median for the following data
x: 10,15,18,23,27,30,31 f
20,30,40,50,60,70
A Cobb–Douglas production function is given by
Assuming that capital, K, is fixed at 100, write down a formula for Q in terms of L only. Calculate the marginal product of labour when
(a) L=4
(b) L=25
(c) L=10000
Verify that the law of diminishing marginal productivity holds in this case.
If the demand function is P = 70 - Q find an expression for TR in terms of Q.
(1) Differentiate TR with respect to Q to find a general expression for MR in terms of Q. Hence write
down the exact value of MR at Q = 60.
(2) Calculate the value of TR when
(a) Q=60
(b) Q=61
and hence confirm that the 1 unit increase approach gives a reasonable approximation to the exact value of MR obtained in part (1).
