The family of functions y = ce^{-2x} + e^{-x} is solution of the equation y' + 2y = e^{-x}. find the constant c which defines the solution which also satisfies the initial condition y(3)= 3.

Step-by-step explanation:

We have the following solution:

We want to find the value of x that satisfies the following condition:

y(3) = 3.

This means that when x = 3, y = 3. So

answer:

1. 0.04

2. 0.15

step-by-step explanation:

i just finished that assignment for properties of probability distributions.

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.