Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #1 Help Me ! » Optimization question? » 2010-11-16 06:45:23

Prakash Panneer
Replies: 2

A commercial pear grower must decide on the optimum time to have fruit picked and sold. If the pears are picked now, they will bring \$0.30 per pound, with each tree yielding an average of 60 pounds of salable pears. If the average yield per tree increases 6 pounds per tree per week for the next 4 weeks, but the price drops \$0.02 per pound per week, when should the pears be picked to realize the maximum return per tree? What is the maximum return?

## #3 Help Me ! » Age problem_Urgent » 2009-07-01 16:04:11

Prakash Panneer
Replies: 2

Two days ago, Sam was fifteen. On the next year, he will be 18. What is his B'day and today's date?

Yes, Tb is higher. Since here we used summation notation.

Prakash Panneer
Replies: 2

4.  Ternary Huffman. Trimedia Disks Inc. has developed ternary hard disks. Each cell on a disk can now store values 0, 1, or 2 (instead of just 0 or 1). To take advantage of this new technology, provide a modified Huffman algorithm for compressing sequences of characters from an alphabet of size n, where the characters occur with known frequencies f1, f2, . . . , fn. Your algorithm should encode each character with a variable-length codeword over the values 0, 1, 2 such that no codeword is a prefix of another codeword and so as to obtain the maximum possible compression. Prove that your algorithm is correct.

5.  The basic intuition behind Huffman's algorithm, that frequent blocks should have short encodings and infrequent blocks should have long encodings, is also at work in English, where typical words like I, you, is, and, to, from, and so on are short, and rarely used words like velociraptor are longer.

However, words like fire!, help!, and run! are short not because they are frequent, but perhaps because time is precious in situations where they are used.

To make things theoretical, suppose we have a file composed of m different words, with frequencies
f1, . . . , fm. Suppose also that for the ith word, the cost per bit of encoding is Ci. Thus, if we find a prefix-free code where the ith word has a codeword of length li, then the total cost of the encoding will
be (summation) i  fi  Ci  li.

Show how to modify Huffman's algorithm to find the prefix-free encoding of minimum total cost.

6.  A server has n customers waiting to be served. The service time required by each customer is known in advance: it is ti minutes for customer i. So if, for example, the customers are served in order of increasing i, then the ith customer has to wait  (summation)( j = 1 to i) tj minutes.

We wish to minimize the total waiting time

T = (summation((i = 1 to n) (time spent waiting by customer i)

Give an efficient algorithm for computing the optimal order in which to process the customers.

This is urgent.

## #6 Help Me ! » Statistics » 2008-12-12 01:17:37

Prakash Panneer
Replies: 1

The cafateria was accused of cheating students bynot giving them enough coffee in their 12oz cups. 15 cups were selected randomnly, they had a mean of 11.7 with a std dev of 0.5 at 0.01 significance level the claim that the customers were being cheated.

Prakash Panneer
Replies: 1

18 people are randomly selected with a mean score of 550 and a std. dev. of 140. Find the 95% confidence interval for the population variance and std.

can you tell me how i find point estimates for population variance and standard deviation?

Thanks a lot

Do we have to find the equation of the two semi circles then add them?

or do we need enough to find the first semi circle based on the limit as 0 to 2?

Prakash Panneer
Replies: 5

[img]C:\Documents and Settings\Prakash\Desktop\Image.JPG[/img]

Find the integral of f(x) whose limit is 0 to 2.

The graph is supposed to look like two semicircles starting at the origin and ending at 6.

## #11 Help Me ! » Calculus » 2008-12-01 10:21:52

Prakash Panneer
Replies: 1

Show that    lim          Sinx = 0
x--> infinity

and              lim          Cosx = 0
x--> infinity

## #12 Re: Help Me ! » find x » 2008-11-11 10:36:22

What my answer is right only.
for example...

a^3 = a^x

We can take x = 3, since the bases are equal.

Similarly we can solve the given problem.

2^(x+2) 5^(6-x) = 10^(x^2)
= (2 x 5)^(x^2)
=2^(x^2) 5^(x^2)

Compare LHS and RHS

x + 2 = x^2         and             6 - x = x^2
x^2 - x - 2 = 0                         x^2 + x - 6 = 0

x = 2, -1   and x = 2, -3

## #13 Re: Help Me ! » vertices » 2008-11-11 09:37:00

A corner point of a geometric figure. For a polygon, vertices are where adjacent sides meet. For an angle, the vertex is where the two rays making up the angle meet.

Note: If the figure is a curve or surface, the vertices are the points of maximum curvature.

## #14 Re: Help Me ! » find x » 2008-11-11 09:34:25

Given that

2^(x+2) 5^(6-x) = 10^(x^2)
= (2 x 5)^(x^2)
=2^(x^2) 5^(x^2)
Compare the LHS and RHS

x + 2 = x^2         and             6 - x = x^2
x^2 - x - 2 = 0                         x^2 + x - 6 = 0

x = 2, -1   and x = 2, -3

## #15 Help Me ! » Help me! » 2008-11-11 02:34:44

Prakash Panneer
Replies: 1

Man pushes a sled horiz to move up a hill.  Weight of girl plus sled is 35kg.  The anlge is 15 deg.  The height is 3.6m.If the sled movves up hill with constant veloxity how much work done by father?

## #16 Re: Help Me ! » Sequences » 2007-09-06 05:00:15

The reason is...

Sequence is the arrangement of numbers which follows a pattern.

The rule behind the arrangement of numbers is called Pattern.

That is, the relation between the those number.

Hope you have understood this one.

## #17 Help Me ! » Mixture problem » 2007-08-16 20:49:59

Prakash Panneer
Replies: 1

a time t=0, a tank contains 4 lbs if salt dissolved in 100 gallons of water. Suppose brine, containing 2 lbs of salt per gallon, enters the tank at a rate of 5 gallons per minute. The mixed solution is allowed to drained from the bottowm of the tank at 5 gallons per minute. find the amount of salt in the tank after 10 minutes

I need the solution and similar kind of problems please

## #18 Re: Help Me ! » Integration » 2007-08-16 20:10:24

Well.

Actually, we have to integrate cos(x^2).

This is the original problem.

## #19 Help Me ! » inverse function » 2007-08-16 20:08:45

Prakash Panneer
Replies: 1

Find the inverse function.

f(x) = x^3+2x-1

## #20 Help Me ! » Integration » 2007-08-16 18:43:33

Prakash Panneer
Replies: 3

integral of (cosu/sqrt root of u) = ?

## #21 Help Me ! » Integers » 2007-08-01 04:32:01

Prakash Panneer
Replies: 6

a, b, c are three integers satisfying the following properties:
1. 0 < a < b < c < 10000
2. a, b, c are all perfect squares.
3. a, b, c are in Geometric Progression.
What is the maximum possible value of a ?

## #22 Re: Help Me ! » Help me!!!!!!!!!! » 2007-07-15 08:36:38

I need justification(Using Box and Whisker plot). Please!!!!

## #23 Help Me ! » Help me!!!!!!!!!! » 2007-07-15 01:27:58

Prakash Panneer
Replies: 5

Median salaries for two companies are \$35,000 and \$40,000. What additional info would be helpful to have before deciding which company you would like to work for?

## #24 Help Me ! » Clock Problem » 2007-07-03 06:48:19

Prakash Panneer
Replies: 2

if the length of the hour and minute hand of a clock are 3 cm and 8 cm respectively. What is the distance in cm, between the tips of the hands at 2 O' clock?

## #25 Help Me ! » Algebra. » 2007-06-12 08:59:29

Prakash Panneer
Replies: 3

Father is aged three times more than his son Rohit. After 8 years, he would be 2 and half times of Rohit's age. After further 8 years how many times would be Rohit's age.

I have a doubt in the first statement.

F = 3 R. Is this right?