Mathematishan

An AHU (Air handling unit) removes an heat load of say 10000 BTU from an office over a period of 200 (25 x 8) hours office operation (this BTU is measured by BTU meter)

The chiller which supplies the cold water to AHU has an power consumption of 1.1 KW/ TR (air cooled condensor which is part of chiller package)

how much units of electric power (KWH) do we pay for.

x^7 + 14 x^5 + 16 x^ 3 + 30 x - 560 = 0

Answers required without use of graphs

1) How many words can be formed using all 8 letters of word DAUGHTER with no repetition of letter allowed and vowels are located in odd position?

2) How many words can be formed using all 8 letters of word DAUGHTER with no repetition of letter allowed and vowels are located in even position?

The above two questions are to be solved as separate questions without actually tabulating and counting and should be simple enough to be explained to a student to whom the subject has introduced recently (say std x)

Also a small variation (please mention logic used)

3) How many such 5 letter words can be created using letters of word DAUGHTER with no repetition of letter allowed and vowels are located in odd position?

4) How many such 5 letter words can be created using letters of word DAUGHTER with no repetition of letter allowed and vowels are located in even position?

1) What is the maximum value of y = sin^ 8 x + cos ^14 x . Here I am not looking at a solution using calculus ( ie using dy/dx = 0) I understand a pure trigonometry solution exists. Can someone help

2) ∫[ (cos x) / (cos 4x)] dx

I understand that there is a simpler method to solve than expressing cos 4x in terms of sinx and substituting sinx = t and integrating ?

1) ABC is a triangle (lying in first quadrant) such that A and B lies on the X and Y axis respectively and C lies on the non origin side of AB. What (geometric figure) is the locus of the point C when seg AB slides like a ladder with end points on both the axes [Point A moves from (0, 0) to (l(AB), 0) on the coordinate axis with B moving from (0, l(AB) to (0, 0)]

Appears that locus is a straight line but was looking for a analytical proof

2)Take n equidistant points on the unit circle. Pick one of those points, then draw chords from it to all other points on the circle, What is the product of lengths of those chords

(Answer can be proved using knowledge of complex numbers but is there a simpler way)

3) Prove that Area of a triangle formed by the three points on a parabola is twice the Area of the triangle formed by three tangents at these points

Postings ome questions from another site

1. Solve : 2 tan x = 4x - 2 sin 2x cos 2x tan² x

2. Show that the solutions of the equation tan ax = tan bx, a² + b² <> 0 are in A.P. Find the common difference of the series.

3. If α , β be the roots of the equation a cos 2θ + b sin 2θ =c then show that

tan α + tan β = 2b / (c + a) and tan α tan β = (c - a) / (c + a)

Prove that the circumcircle formed by any three tangents to parabola always pass through its focus.

would like a proof without using coordinate geometry (although that is also welcome)

If I am given the lengths of the 3 altitudes of a triangle (say I take at random altitude 6cm, 7cm, 8 cm)

a) can i construct a triangle using pure construction methods (w/o calculating sides)

b) how would I do it by calculating sides

given 3 altitudes is the traingle formed unique

answers or good links to sites explaining answers are also welcome

1) If a and b are distinct integers and n is a natural no. prove that

{[2^(2n-1)][a^(2n) + b^(2n)] - (a + b)^(2n) } / [(a -b)^2] is an integer

2) For each integer n > 1, prove that n^n - n ² + n -1 is divisible by (n -1) ²

for BA - I would request these to be proved without using principles of Mathematical Induction

However all proofs are welcome

http://in.answers.yahoo.com/question/index?qid=201...

In the attached question asked by my son a student of Std ix , I would like to know the following

a) what is the min area (210?? 220??) that needs to be specified for the triangle for the answer to be correct.

I have a vague feeling we may need more qualifications for this triangle (isosceles right, equilateral etc) for this min area to be specified in the question.

b) Another related question - for a given perimeter of triangle do we have a min area of Circumcircle (not Incircle)

Lastly the link above appears to be a question for pre engg exam preparation - not sure what a student is supposed to answer here ? any idea

a)Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat. He says to you, "Do you want to pick door number 2?" Is it to your advantage to switch your choice of doors?

b)If 8 chocolates are distributed among 11

students, find the chance that a particular

student receives 5 chocolates.

c)25 persons were invited for a party by a host.

What is the probability that two particular persons

be seated on either side of the host at a circular table

I don't want to tell my son (std V1 - age 11) that a gun when fired recoils by using reasons like say Newtons 3rd law or law of conservation of momentum How would I explain him (They are not, in any case, the reasons for recoil. How can I explain him or I cant ? (he understands forces but not energy)

ABC is an isosceles triangle such that angle B = 100° and AB = BC.

extend BA to D such that BD = AC (or B-A-D)

Join DC and Find angle ACD

A circular grass field has circumference = 22m. A goat with a rope round the neck is located such that the other end of the rope is hooked to a on a point on the circumference. what should be the length of a rope so that the goat can only graze half the area of the circular field.

additionally web links to similar problems or topic will also help

My sons school has invited me to deliver a workshop/lecture for ix and x students on how to study Physics , Chem and Mathematics - Some tips, ideas, math examples, links, stories to tell, approaches to take to make this informative/educative for students shall help a lot. Duration 2 hrs, The subject covered IN Maths are Geometry, Trigo, AP GP,Basic Probability, Algebra, Precalculus, Stats, Physics include motion, Newtons law, Archemdies, heat, electricty Magnetism, light etc, chemistry has metals, organic, inorganic etc

Let ABC be an isoceles Δ (AB = AC) with angle BAC = 20° Point D is on side AC such that angle DBC = 60°. point E is on side AB such that angle ECB = 50°,

Find with proof the measure of angle EDB