Consider the initial value problem my" + cy' + ky = f(t), y(0) = 0, y'o) = 0 modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force f(t), where the unit of force is the newton (n). assume that m = 2 kilograms, c = 8 kilograms per second, k = 80 newtons per meter, and f(t) = 50 sin(6) newtons. a. solve the initial value problem. y(t) = (25/(6t)-6cos(6t))e^(2t)+sin(6t)+co s(6t))^(-2t) (formulas) b. determine the long-term behavior of the system. is lim y(t) = 0? if it is, enter zero. if not, enter a function that approximates y(t) for very large positive values of t. for very large positive values of t, y(t) t (formulas)

answer: 457.14

step-by-step explanation:

205 - 45 = 160

160 / .35 = 457.142857

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

answer: 5100 just subtract

step-by-step explanation:

in geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. by extension, a line and a plane, or two planes, in three-dimensional euclidean space that do not share a point are said to be parallel.