We use the binomial theorem to answer this question. Suppose we have a trinomial (a + b)ⁿ, we can determine any term to be:
[n!/(n-r)!r!] a^(r) b^(n-r)
a.) For x⁵y³, the variables are: x=a and y=b. We already know the exponents of the variables. So, we equate this with the form of the binomial theorem.
r = 5
n - r = 3
Solving for n,
n = 3 + 5 = 8
Therefore, the coefficient is equal to:
Coefficient = n!/(n-r)!r! = 8!/(8-5)!8! = 56
b.) For x³y⁵, the variables are: x=a and y=b. We already know the exponents of the variables. So, we equate this with the form of the binomial theorem.
r = 3
n - r = 5
Solving for n,
n = 5 + 3 = 8
Therefore, the coefficient is equal to:
Coefficient = n!/(n-r)!r! = 8!/(8-3)!8! = 56
Sample Response: This phenomenon is called chromatic aberration. This happens when light of different wavelengths focuses at different points. A converging lens is used to help light of different wavelengths focuses at a common point.
Actually Welcome to the concept of resistors,
The equivalent circuit is given as,
1/Rp = 1/3 + 1/6 + 1/9
1/Rp = 6+3+2/18
1/Rp = 11/18
Rp = 18/11 ==> 1.63 ==> 1.6 ohms
hence the equivalent resistance of the circuit is 1.6 ohms
