Messages posted by umesh

root(2) -1 =1/(root(2)+1)

root(2)+1 = 1/tan(pie/n)

2*root(2)=tan(pie/n)+1/tan(pie/n)

root(2)=(1+tan^2(pie/n))/2tan(pie/n)

1/root(2)=sin2pie/n

2pie/n = pie/4

n = 8

say '

y=tan inv {(1-x)/(1+x)}

y=tan^-1(pi/4-x)

dy/dx= -1/(1+(pi/4-x)^2) ---- 1

say t= sin inv(3x-4x^3)

dt/dx= (1/root(1-(3x-4x^3)^2)) *(3-12x^2)--2

divide 1/2 you will get the answers

INORGANIC CHEMISTRY

NCERT Inorganic Chemistry
Concise Inorganic Chemistry by J.D. Lee
IIT Chemistry by O.P. Aggarwal

I have just put n=1,2,3,4,5,6--- and checked it if it is satisfy.

This hospital management system has the software applications that are capable of handling the activities of following major departments:

1. Outdoor patient's Department
2. Indoor Patient's Department
3. Investigative Labs
4. Billing
5. Medical Stores
6. Financial Accounting
7. Payroll

The Hospital Management system is developed in Visual Basic with MS SQL server as database system. The operating platform for the operation is Local Area Network operating with Window NT.

cosx cos(sinx)

put 2x+2 =t

4(x^2+2x+1)=t^2

4x^2+8x+13 =t^2+9

8(x+1)=2t

4(x+1)dx=dt

subtitute and you will get a answer.

Solution is already given

http://www.goiit.com/posts/list/algebra-find-the-sum-of-all-3-digit-nos-which-have-atleast-one-993967.htm

(n-1)n(n+1)(n+2)=5040

(n^2+2n)(n^2-1)=5040

n^4+2n^3-n^2-2n=5040

n=8 satisfy the equation

hence the numbers are 7,8,9 and 10

I think compelete question is

A horizontal force F=mg/3 is applied on the upper surface of a uniform cube of mass m and side a which is resting on a rough horizontal surface having co-eff. of friction = 1/2. The distance between the lines of action of mg and normal reaction is:
A. a/2
B. a/3
C. a/4
D. none of these

Solution:

On balancing the moments about centre of gravity, we get
mg (a/2) + mg(a/3) = mg (a/2+x)
Therefore, on solving we get, x=a/3.
Ans is (b)

1.Rhinoceros

2. American tapir

3. African Zebra

he chemical structure of everyone's DNA is the same. The only difference between people (or any animal) is the order of the base pairs. There are so many millions of base pairs in each person's DNA that every person has a different sequence.

Using these sequences, every person could be identified solely by the sequence of their base pairs. However, because there are so many millions of base pairs, the task would be very time-consuming. Instead, scientists are able to use a shorter method, because of repeating patterns in DNA.

These patterns do not, however, give an individual "fingerprint," but they are able to determine whether two DNA samples are from the same person, related people, or non-related people. Scientists use a small number of sequences of DNA that are known to vary among individuals a great deal, and analyze those to get a certain probability of a match.

oot (a^ - 4)tanA+a tanB+ root (a^2 + 4)tanC>= 3(const tanAtanBtanC)^(1/3)

where const = a*root (a^a - 4)*root (a^2 + 4)

(2a)^3 /const >=tanAtanBtanC

8a^2/root((a^2 - 4)(a^2 + 4)) >=tanAtanBtanC

8a^2/root(a^4 -16)>=tanAtanBtanC

Now the maximum value of tanAtanBtanC is 8a^2/root(a^4 -16)

Now

tan^2A+tan^2B+tan^C>=3(tanAtanBtanC)^(2/3)

since it must be greater than its maximum value

minimum value is

3(8a^2/root(a^4 -16))^2/3 = 12 (a^4/root(a^4 -16))^(1/3)

lets the equation of the hyperbola is (x/a)^2-(y/b)^2=1

the equation of tangent is

xx1/a^2 -yy1/b^2 =1

it will pass through locus (h,k)

hx1/a^2 - ky1/b^2=1

hx2/a^2 -ky2/b^2=1

solve for h and k you will be able to find out the locus .

let me know if you have any further difficulties

Correct my understanding If I am wrong

If we can predict that what is the roots of denominator part we can easily be able to find out the lower fractions of denominator part and hence number of partial fractions that the function have.

I think You meant t ask difinite integral

of " log ( 1+tanx) "

from x= 0 to x= pi/4.

If it is so then

put integrap property

I = log ( 1+tan(pi/4-x))

I = log2 - log(1+tanx)

add oroginal and this one

I =(log2)/2

a.The average slope = [f(4) - f(-4)]/[4 - (-4)]

f(4)=244

f(-4)=-244

average slope is (488/8)=61

b.

f'(c) = 61

f'(x)=12x^2-3

12x^2-3 =61

12x^2=64

x= 4/root(3) and -4/root(3)

lets talk abt 0=<x<=pi

at x the value of y is sinx

at pi-x value of y is sin(x)

hence area is

A= (pi-2x)sinx

for mximum value

dA/dx=0

(pi-2x)cosx -2sinx =0

Now you can proceed further

tanx = pi/2-x

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