hussain34
18.03.2020 •
Mathematics
Use the binomial theorem to find the coefficient of xayb in the expansion of (5x2 + 2y3)6, where a) a = 6, b = 9. b) a = 2, b = 15. c) a = 3, b = 12. d) a = 12, b = 0. e) a = 8, b = 9.
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Ответ:
The coefficients of xᵃyᵇ for respective given values of a and b have been provided below.
We are given the expression;
(5x² + 2y³)⁶
Using online binomial expansion calculator gives us;
15625x¹² + 37500x¹⁰y³ + 37500x⁸y⁶ + 20000x⁶y⁹ + 6000x⁴y¹² + 960x²y¹⁵ + 64y¹⁸
We want to find the coefficient of xᵃyᵇ in the binomial expansion;
1) When a = 6 and b = 9, the coefficient is 20000
2) When a = 2, b = 15; the coefficient is 960
3) When a = 3 and b = 12; there is no coefficient
4) When a = 12 and b = 0; the coefficient is 15625
5) When a = 8 and b = 9; there is no coefficient.
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Ответ:
Step-by-step explanation:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 6 15 20 15 6 1
we use these for the expansion of (5x² + 2y³)⁶
1(5x²)⁶(2y³)⁰ + 6(5x²)⁵(2y³)¹ + 15(5x²)⁴(2y³)² + 20(5x²)³(2y³)³+ 15(5x²)²(2y³)⁴+ 6(5x²)¹(2y³)⁵ + 1(5x²)⁰(2y³)⁶
78125ₓ¹²+187500ₓ¹⁰ y³ +37500ₓ⁸y⁶+20000ₓ⁶y⁹+6000x⁴y¹²+960x²y¹⁵+2y¹⁸
a.)a = 6, b = 9. the coefficient of xᵃyᵇ ( 20000ₓ⁶y⁹) = 20000
b) a = 2, b = 15. the coefficient of xᵃyᵇ ( 960x²y¹⁵) = 960
c) a = 3, b = 12. the coefficient of xᵃyᵇ is not present
d) a = 12, b = 0 the coefficient of xᵃyᵇ ( 78125ₓ¹²) = 78125
e) a = 8, b = 9. the coefficient of xᵃyᵇ is not present
Ответ:
Transitive.
Step-by-step explanation:
Transitive property says: if a = b ; b = c then a = c.
So, transitive property is used to prove the equality between to variables using one in common. In this case, to prove VQT = WRS you need to considerer the common angle to use this property, which is angle SQU.
So, VQT = SQU ; SQU = WRS
Hence, VQT = WRS.