Math Answers

show that y=c1e^x+c2e^2x is the general solution of y''-3y'+2y=0 on any interval, and find the particular solution for which y(0)=-1 and y'(0)=1

1. Let f be the function deÖned by

f (x) = x^2/(-2x + 1)^2

(a) Determine the vertical and horizontal asymptotes (show all limits).

(b) Use the sign pattern for f'(x) to determine

(i) the interval(s) over which f rises and where it falls;

(ii) the local extrema.

(c) Use the sign pattern for f''(x) to determine

(i) where the graph of f is concave up and where it is concave down.

(ii) the inflection points (if any)

Write true if the statement is true

Write false if the statement is false

1.the amount of an employees gross earnings is the total amount that he or she earns in a specific period.

2.the net earnings of an employee are the sun of his or her gross earnings and the total deductions.

3.the minimum wage in a certain region refers to the latest amount that a worker in that region should receive in exchange for a rendered service.

4.a seperation pay must be given to an employee who was dismissed from a company due to a crime that the employee committed.

5.a night shift differential refers to the additional compensation a wage earner receives for working between 9pm to 6 am.

6.a maternity leave benefit is given to all married employees who sre pregnant.

7.a holiday pay refers to the additional compensation required by law for work performed within 8 hours on nonworking regular days.

.

.

A coke float machine dispenses into 18-ounce cups. Test show that the actual amount of ice cream dispensed is normally distributed with a mean of 12.75 oz. and a standard deviation of 0.27 oz.

a. what percent of cups will receive 12.25 oz of ice cream?

b. wha percent of cups will receive less than 12.15 oz. of ice cream?

Locate and classify all critical points for f(x, y) = 4y^2x + 3xy

F ind aba -1 w here (i) a = (5 , 7 , 9) , b = (1 , 2, 3) (ii) a = (1 , 2,5)(3 , 4) , b = (1 , 4 , 5)

Given the data 6, 9, 12, 15, 16, 19, 22. Construct a sampling distribution of the sample mean without replacement and repetition by selecting 2 samples at a time.

Determine the present value of a loan if R12 000 is due in ve years' time, at a simple dis

ount rate of 15%

per annum.

[1℄ R12 656,25

[2℄ R12 972,97

[3℄ R13 125,00

[4℄ R13 664,28

Prove that \sum_{i=0}^{n} 2^{i} = 2^{n + 1} - 1 Use mathematical induction for this proof and discuss/explain each step.

If A={1,3,5,7} and B={1,3,7}. Is set B a proper subset of set A? Explain.