Answer:
3,247,695
Step-by-step explanation:
We want the coefficient of the term with x^8
So Use Newton's Binomial Expansion formula
Formula is (x + y) ^n = Sum for i=0 to n (n choose i) x^(n-i)*y^i
here (x^2 + 3) ^ 12
( 12 choose i) * (x^2)^(12-i) * (3)^i
i needs to equal 8 for us to get x^8
(12 choose 8) * (x^2)^(12-8) * (3^8)
= (12 choose 8) * x^8 * (3^8)
so a = (12 choose 8) *
a = (12! /(8! * 4!) ) *
a = ( 12*11*10*9/ 4*3*2*1) *
a = (11*5*9) *
a = 11*5*9 * 6561
a = 3,247,695
Alright, lets gets started.
If water enters through a pipe alone, swimming pool can be filled in 12 hr.
Or say, in 12 hrs, swimming pool can be filled with help of pipe.
It means in 1 hr, the part of swimming pool filled = (For pipe only)
Similarly, with hose only, , in 1 hr, the part of swimming pool filled =
So, water is coming from both, pipe and hose , then in 1 hr, the part of pool filled will be =
Suppose in x hrs, with both supplies, pipe and hose, pool is filled.
Means
making common denominator
Flipping
Means 8.57 hrs : Answer
Hope it will help :)
To solve for x in terms of b, simply treat b as a number, and solve for x as usual: first of all, we expand the left hand side:
Subtract 10 from both sides:
Divide both sides by -2b:
This means that in particular, if we set , we have