For the following functions, find the differential operator l that annihilates the given function. you may write the operator in factored form, and you must make the degree of the operator as low as possible and make the leading coefficient 1. for example, l= (d – 1)(d – 2) annihilates y = 3e2 + 17e2x. in other words, the function y = 3ex + 17e2x is a solution to the linear homogeneous ode with constant coefficients l[y] = (d – 1)(d – 2)[y] = 0. (a) l = (d+2)(d-1) annihilates y = 9e-2x + 5elx. (b) l= annihilates y = -6x3e-6x (c) l = (d-4)^2+(2)^2 annihilates y = 241 sin(2x). (d) l = annihilates y = 3x4 cos(5x) – 2x2 sin(5x) – x²e-4x.

Five number summary is:

Minimum Value = 32

First Quartile = 56

Median = 69.5

Third Quartile = 80

Maximum Value = 99

Box plot is used to represented by Option C.

Step-by-step explanation:

The box plot is made up of five number summary.

The five number summary consists of:

Minimum Value

First Quartile

Median

Third Quartile

Maximum Value

So, Looking at the data set and finding five number summary,

Minimum Value = 32

First Quartile

We find median of lower half of data (i.e all data before median)

(55+57)/2 =112/2 =56

So, First Quartile = 56

Median

Mean of middle most numbers: 69+70/2 = 69.5

So, Median = 69.5

Third Quartile

We find median of upper half of data (i.e all data after median)

(79+81)/2 =160/2 =80

So, Third Quartile = 80

Maximum Number = 99

So, Five number summary is:

Minimum Value = 32

First Quartile = 56

Median = 69.5

Third Quartile = 80

Maximum Value = 99

Box plot is used to represent this five number summary.

Option C is correct.