Answer with Step-by-step explanation:
Let a mass weighing 16 pounds stretches a spring
feet.
Mass=
Mass=

Mass,m=
Slug
By hook's law




A damping force is numerically equal to 1/2 the instantaneous velocity

Equation of motion :

Using this equation



Auxillary equation





Complementary function

To find the particular solution using undetermined coefficient method



This solution satisfied the equation therefore, substitute the values in the differential equation


Comparing on both sides


Adding both equation then, we get


Substitute the value of B in any equation



Particular solution, 
Now, the general solution

From initial condition
x(0)=2 ft
x'(0)=0
Substitute the values t=0 and x(0)=2




Substitute x'(0)=0




Substitute the values then we get

In order to calculate the number of loaves Roger can bake, we should calcculate how many times 3/4 (required butter for one loaf of bread) is included in 2 1/2 (amount of butter Roger has).
2 1/2=4/2+1/2=5/2
(5/2)/(3/4)=5*4/2*3=20/6=3,33
Roger can bake 3 loaves of bread.
Answer:
There are an absolute minimum (x = 6) and an absolute maximum (x = 12).
Step-by-step explanation:
The correct statement is described below:
Find the absolute maximum and minimum values of the function below:
, 
Given that function is a polynomial, then we have the guarantee that function is continuous and differentiable and we can use First and Second Derivative Tests.
First, we obtain the first derivative of the function and equalize it to zero:


(Eq. 1)
As we can see, only a solution is a valid critical value. That is: 
Second, we determine the second derivative formula and evaluate it at the only critical point:
(Eq. 2)
x = 6

(Absolute minimum)
Third, we evaluate the function at each extreme of the given interval and the critical point as well:
x = 2


x = 6


x = 12


There are an absolute minimum (x = 6) and an absolute maximum (x = 12).
Answer:Y=3/1 X -1
Step-by-step explanation:rise over run 3/1 and then y intercept is -1