Question

answer this very fast plz it's urgent​

Answer 1

Answer:

On the surface, partition numbers seem like mathematical child's play. A partition of a number is a sequence of positive integers that add up to that number. For example, 4 = 3+1 = 2+2 = 2+1+1 = 1+1+1+1. So we say there are 5 partitions of the number 4.

It sounds simple, and yet the partition numbers grow at an incredible rate. The amount of partitions for the number 10 is 42. For the number 100, the partitions explode to more than 190,000,000.

"Partition numbers are a crazy sequence of integers which race rapidly off to infinity," Ono says. "This provocative sequence evokes wonder, and has long fascinated mathematicians."

By definition, partition numbers are tantalizingly simple. But until the breakthroughs by Ono's team, no one was able to unlock the secret of the complex pattern underlying this rapid growth.

The work of 18th-century mathematician Leonhard Euler led to the first recursive technique for computing the partition values of numbers. The method was slow, however, and impractical for large numbers. For the next 150 years, the method was only successfully implemented to compute the first 200 partition numbers.

Answer 2

➳GIVEN:-

• Particle is projected from the ground with intial speed of V.

• At an angle $\theta$ with horizontal.

➳FIND:-

• Average velocity of particle between between it's points of projection and heighest point of trajectory = ?

➳SOLUTION:-

we know,

$\sf⎆Average \: Velocity = \frac{Displacement}{Time}$

$\sf⎆V_{av} = \frac{ \sqrt{ {H}^{2} + \frac{ {R}^{2} }{4} } }{ \frac{T}{2} }$

where, H = $\sf max^m\:height$

$\sf ➲ H = \frac{V^2sin^2\theta}{2g}$

$\sf ➲ Time \: t = time \: of \: flight = \frac{2Vsin\theta}{g}$

$\sf☄Hence, \boxed{ \sf v_{av} = \frac{v}{2} \sqrt{1 + 3 { \cos }^{2} \theta } }$