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The Smart Treasure Fund was created for Samson after he lost his leg in a battle with pirates. The fund has undertaken to pay him R1 200 000 now. Samson prefers to receive three payments: one three years from now; one twice the size of the first payment six years from now, and one four times the size of the first payment ten years from now. The amount of money to the nearest rand that Samson can expect to receive six years from now if the interest rate applicable is 8,6% per year, compounded quarterly, will be
If
R=x
s
18
¬
0,15
R=xs18¬0,15
is simplified, then the equation becomes
Three years ago Lilly borrowed R10 000 from Faith on condition that she should pay her back two years from now. She also owes Faith R6 000 payable five years from now. The applicable interest rate for both transactions is 13,75% per year, compounded every six months. After considering her payback schedule, Lilly asks Faith if she can pay her R9 000 now and the rest in four years' time. She agrees on condition that the new agreement will run from now and that an interest rate of 16,28% per year, compounded monthly, will be applicable from now. The amount that Lilly will have to pay Faith four years from now is
An interest rate of 14,90% per year, compounded every 3 months, is equivalent to a weekly compounded interest rate of
Three years ago Lilly borrowed R10 000 from Faith on condition that she should pay her back two years from now. She also owes Faith R6 000 payable five years from now. The applicable interest rate for both transactions is 13,75% per year, compounded every six months. After considering her payback schedule, Lilly asks Faith if she can pay her R9 000 now and the rest in four years' time. She agrees on condition that the new agreement will run from now and that an interest rate of 16,28% per year, compounded monthly, will be applicable from now. The amount that Lilly will have to pay Faith four years from now is
3/x+3-2x-6/x^-9x
Find the general solutions of the following differential equations using D-operator methods:
(D + 4)2 x = sinh 4t
Solve for x in the following set of simultaneous differential equations by using D-operator methods:
(D + 2) x - 3y = 1
-3x + (D + ) y = e-t
An organization is interested in the analysis of two products that can be produced from the idle time of labour, machine and investment. It was notified on the investigation that the labour requirement of the first and the second products was 4 and 5 units respectively and the total available man-hours were 48. Only the first product required machine hour utilization of one hour per unit and at present only 10 spare machine hours are available. The second product needs one unit of by-product per unit and the daily availability of the by-product is 12 units. According to the marketing department, the sales potential of the first product cannot exceed 7 units. In a competitive market, the first product can be sold at a profit of Rs.6 and the second product at a profit of Rs.10 per unit. Formulate the problem as a linear programming model. Also determine graphically the feasible region. Identify the redundant constraints if any.
Find the position vector when acceleration a(t)= 2i + j + 3k
#339914 on Dec 2023