A+B=225;; A+B=180+45 ;; -45=180-(A+B) ;; TAKING TAN BOTH SIDES ;;; TAN(-45)=TAN(180-(A+B));;; -1=-TAN(A+B);;
TAN(A+B)=1 ;;; TAN(A) + TAN(B) = 1- TAN(A)TAN(B) ;;; TAN(A)+TAN(B)+TAN(A)TAN(B) = 1 ;; Question was to find {1+TAN(A)}{1+TAN(B)} === 1+ TAN(A) +TAN(B) + TAN(A)TAN(B) == 1+ 1 == 2 Assuming a person can grow a maximum of 40 crore hair on thier body and that the world has a population of 730 crore, What are the chances of 2 people having the same number of body hair on them ?
Looks 1/40 crore. Let the first person grow any number say n of hair. Second person can be anybody growing any number from 1 to 40 crore. The probability of n appearing in 40 crore is 1/40 crore.
The probability here as asked "exactly"
Is actually this
Now , as we know that a leap year has 366 days
This means if we want to have exactly 52 Tuesdays then the remaining two days must not be a Tuesday
The outcomes can be either
(Sun,Mon) (Mon,Tues),(Tues,wed) (Wed,thurs) (thurs,fri) (fri,sat)
(Sat,sun) .now the favourable outcomes are only 5 , therefore it should be 5/7
It is 5/7
Nevertheless I have used a spread sheet to find the 4P3 i.e. 24 three digit numbers. Each column has any digit 6 times. Hence the total of any column is 6*(3+4+6+8) i.e. 126. Writing 6 in the unit place we carry 12 to the second column which again has a total of 126 which makes it 126+12=138. We write 8 in the tens place and carry 13 to the third column. The third column will be 126+13=139 which we have to write as it is. Hence the answer reads 13986.
In a rational number,
twice the numerator is 2 more than the denominator.
If 3 is added to each i.e. the numerator and the denominator, the new fraction is 2/3.
Find the original number?
let the numerator be a and the denominator b. One of the equations is 2a=b+2. The other equation is (a+3)/b+3)=2/3. The solution gives a=7 and b=12. First check 2*7=12+2. Second check (7+3)/(12+3)=2/3
Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively.
What is the ratio of their speeds?
Let the distance between Howrah and Patna be D kilometer and let the trains cross at a distance of x from Howrah. Let us call the train from Howrah to Patna as T1 and other T2 and their corresponding speeds s1 and s2. The remaining distance in case of first train is D-x and in the other x. Since the first train covers its remaining distance in 9 hours and the other in 16 hours s1=(D-x)/9 similarly s2=x/16............(1)
There fore s1/s2=16*(D-x)/(9*x)
Since the two train cross after equal time from the start, their distances covered are in proportion to their speeds.
This gives s1/s2=x/(D-x).................(2)
From equation (1) and (2)
x/(D-x)=s1/s2=16s2/9s1
Cross multiplying gives s1/s2 = 4/3
If length, breadth and height of a room are in the ratio 3:2:1. If the breadth and length are halved, while the height is doubled. Then what is the percentage change in the total area of the 4 walls of the room?
