Solve the inequality and give your answer in interval notati

Solve the inequality and give your answer in interval notation: 5x - x^2 > 0 Determine the 4th term in the binomial expansion of (x^4 + 3y)^10.

Solution

a) 5x - x^2 > 0

x(5 - x) > 0

x > 0

and 5 - x > 0 ======> x < 5

So notation is 0 < x < 5

b) Binomial expansion of (x^4 + 3y)^10 = x⁴⁰ + 30x³⁶y + 405x³²y² + 3240x²⁸y³ + 17010x²⁴y⁴ + 61236x²⁰y⁵ + 153090x¹⁶y⁶ + 262440x¹²y⁷ + 295245x⁸y⁸ + 196830x⁴y⁹ +59049y¹⁰

4th term = 3240x²⁸y³