#$&*
Mth 271
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
preparing for major quiz 1
** **
I am trying to get ready for the major quiz and I cannot find a problem like this one in all the notes. I understand about setting up a system with 3 equations and solving for c, but if I set it up with the given equation, there are no unknowns.
** **
Problem: The quadratic depth vs. clock time model corresponding to depths of 29.16085 cm, 20.06715 cm and 15.7189 cm at clock times t = 13.50989, 27.01979 and 40.52968 seconds is depth(t) = .013 t2 + -1.2 t + 43.
Show the system of equations we would solve to get this model.
Then use the model to determine the average rate which depth changes between clock times t = 39.3 and t = 1039.3 seconds.
What do you think the instantaneous rate of depth change is at clock time t = 39.3 seconds?
I am setting up the system as
29.16085 =(.013)(13.50989)^2- 1.2(13.50989) + 43
20.06715 = (.013)(27.01979)^2 -1.2(27.01979) + 43
15.7189 = (.013)(40.52968)^2 -1.2(40.52968) + 43
This leaves no unknowns to solve for.
I am supposed to ignore the given equation and set it up as
29.16085 = a(13.5089)^2 +b(13.5089) + c
etc. and solve for c?
@&
Exactly, except that of course you'll get three such equations.
*@
@&
Detailed explanation (most of which you already know):
The problems illustrated in the worksheets are very clear that the coordinates are to be substituted into the general form of a quadratic, which is
y = a t^2 + b t + c.
You are asked here to show the system of equations you would use to get the given depth model. You wouldn't use the give depth model to get the given depth model, because you wouldn't be assuming that you already know the model.
That is, you aren't going to use
depth(t) = .013 t2 + -1.2 t + 43
to answer this question.
You plug the y and t coordinates into the form
y = a t^2 + b t + c.
You'll get three equations in a, b and c.
*@
stand exactly how to set up the problem.
#$&*
@&
You are on the right track. You just need to get three equations.
You're reasoned out how to get the equation
29.16085 = a(13.5089)^2 +b(13.5089) + c
You have two more data points, each of which gives you another equation.
*@
@&
The purpose of this problem is to be sure you know how to set up the system to solve for a, b and c. You might not have seen a problem stated exactly like this one, but you've seen all you need to know to answer this question.
*@
@&
Other problems on the Major Quiz might ask you to solve a system and write the model.
On a test I don't want to ask you to go through the entire process, as you did in the homework. This is in order to keep the time required to take the test reasonable.
*@