Chapter 1.4, Problem 16P

PLEASE ANSWER ALL PARTS!!!

PLEASE ANSWER PARTS!!!

Please prove this theorem

2) Find the general solution to the differential equation d²x dt² 2 dax = dt

Show how continued fractions connect the golden ratio to the Fibonacci sequence

Let X and Y be independent random variables both with the same mean µ=0. Define a new random variable W = aX +bY, where a and b are constants.

12. Suppose that a, b E R and a < b. Show that the vector space C[a, b] of all continuous complex valued functions defined on [a, b], with supremum norm is a Banach space. Ilflloc: = sup f(t), t€[a,b]

Solve the following systems using Gauss Seidal and Jacobi iteration methods for n=8 and initial values Xº=(000). - 3x1 + 2x2 x3 = 4 - 2x1 x2+2x3 = 10 x13x24x3 = 4

A gardener has ten different potted plants, and they are spraying the plants with doses offertilizers. Plants can receive zero or more doses in a session. In the following, we count eachpossible number of doses the ten plants can receive (the order of spraying in a session doesnot matter). How many ways are there to do two sessions of spraying, where each plant receives atmost two doses total?