A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
The change in water level of a lake is modeled by a polynomial function, W(x). Describe how to find the xintercepts of W(x) and how to construct a rough graph of W(x) so that the Parks Department can predict when there will be no change in the water level. You may create a sample polynomial of degree 3 or higher to use in your explanations.
anonymous
 one year ago
The change in water level of a lake is modeled by a polynomial function, W(x). Describe how to find the xintercepts of W(x) and how to construct a rough graph of W(x) so that the Parks Department can predict when there will be no change in the water level. You may create a sample polynomial of degree 3 or higher to use in your explanations.

This Question is Closed

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1a general formula for a polynomial of third degree can be this: \[\Large W\left( x \right) = A{x^3} + B{x^2} + Cx + D\] where A, B, C, and D are real coefficients

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok. Know what do I do?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1in order to determine those coefficients, we need to know some data about the water level of your lake. Do you have a table which collects the water level of the lake in function of time?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No. That was the whole question. That's why I was confused :(

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1if we draw a graph in which time x is along the horizontal axis, and the water level W(x) is along the vertical axis, then the xintercept, is the month at which W(x)=0

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1So a way to establish the xintercept, is to record at which month, the water level W(x)=0

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1the complete answer should report the values of each coefficient A, B, C, and D, and the followed procedure to get those values. Nevertheless, without any data about the water level of the lake, we are not able to evaluate those coefficients

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what about the last part? Should we create an imaginary problem with a degree higher than 3?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1Using a polynomial whose degree is greater than 3, involves many real coefficients whixh have to be determined. For example, if we conjecture a polynomial of degree 4, then we can write: \[\Large W\left( x \right) = {A_1}{x^4} + {A_2}{x^3} + {A_3}{x^2} + {A_4}x + {A_5}\] As you can see, now we have to determine, by using our experimental observations, 5 real coefficients, namely: \[\Large {A_1},\;{A_2},\;{A_3},\;{A_4},\;{A_5}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ahhh I understand! Ok so thats the final answer, correct?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1yes! You can write this: "We can establish the values of each coefficients of our sample polynomial function for W(x), by experimental observations about the water level W(x) as function of time or as function of the months of the year"

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I think that better is if we make a drawing of that function: \[\Large T\left( x \right) = {\left( {x  4} \right)^3} + 6\] That function is represented by a cubic parabola

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1here is the corresponding graph:

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1as we can see the turning point is at x=4. At x=4 the temperature is: \[\Large T\left( 4 \right) = {\left( {4  4} \right)^3} + 6 = 0 + 6 = 6\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1yes! I think so!

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1The requested experimental procedure, which can be used in order to find that turning point, can be this: "We substitute many values for the x variable, when a change in x, produces little change in T(x), then we are close to that turning point"

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I honestly wanna say thankyou for all of your help::)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry, I have one last question!

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I'm pondering...

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1as stated in the previous exercise, a turning point can be like a vertex of a parabola, or a quadratic function

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1so, Tucker and Karly are both correct, if they refer to a graph like this: dw:1436024150337:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1dw:1436024243604:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1dw:1436024282359:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0OHHH So how could we write that into an equation for the both of them?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1dw:1436024389509:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i understand how to do it now but I just don't know how to put it into words, if that makes sense.

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1a possible sentence is like this: "Tucker and Karly are saying the same thing, so they can both be correct, if they refer to a graph like this, for example:" dw:1436024700576:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ohh :) Thankyou once again!!!!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Are you up for one more?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1That graph is a polynomial of fourth degree: \[\large P\left( x \right) = {x^4}  {x^3}  11{x^2} + 9x + 18\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1In order to establish the point x such that P(x)=0, we have to factorize those function P(x). Do you know how to factorize that function?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeas. Would it be x32x29x+18?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1better is: \[{x^4}  {x^3}  11{x^2} + 9x + 18 = \left( {x + 1} \right)\left( {{x^3}  2{x^2}  9x + 18} \right)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wow. I can't believe I got that right! Usually I get those equations wrong. R u sure lol? I mmay have gotten that wrong

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now, we can factorize the polynomial: x32x29x+18, so the complete factorization of P(x) is: \[\large {x^4}  {x^3}  11{x^2} + 9x + 18 = \left( {x + 1} \right)\left( {x + 3} \right)\left( {x  3} \right)\left( {x  2} \right)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i see, I see. Now what do we do?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now the points x, such that P(x)=0, are given by the subsequent conditions: x+1=0 >x=1 x+3=0 > x=3 x3=0 >x=3 x2=0 > x=2

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now, since x is a profit, then it has to be a positive number, so our acceptable solutions are: x=2, and x=3

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1yes! it is the second part, we have to answer to the first part

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wouldn't we factor x32x29x+18?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1yes! I have factored that polynomial

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1\[{x^3}  2{x^2}  9x + 18 = \left( {x  2} \right)\left( {x + 3} \right)\left( {x  3} \right)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so would it be (x2)(x+3)(x3) as an answer?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh okay now what do we do?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1as I wrote before, the complete factorization is: \[\left( {x + 1} \right)\left( {x + 3} \right)\left( {x  3} \right)\left( {x  2} \right)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now we have to answer the 2nd part yes?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1we have to say the graph type which represents our original polynomial: \[{x^4}  {x^3}  11{x^2} + 9x + 18\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So what would the graph look like?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1here is my reasoning:

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1let's consider the point x=2 for exmple

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1if we substitute x=2.1, into the equation of P(x), we get a negative quantity, since, we have: x2>2.12 = 0.1 >0 x+1> 2.1 +1 =3.1 >0 x3> 2.13=0.9 <0 x+3> 2.1+3=5.1 >0 then the product: \[\left( {x + 1} \right)\left( {x + 3} \right)\left( {x  3} \right)\left( {x  2} \right)\] is negative

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohhh I see. How would we graph w/o technology?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I think that the subsequent reasoning is better: since our graph has to pass at subsequent points: \[\left( {  3,0} \right),\;\left( {  1,0} \right),\;\left( {2,0} \right),\;\left( {3,0} \right)\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1necessarily it is a s follows: dw:1436026592697:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0:) Thankyou so much you're a lifesaver!!!!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how long will u be on here? I may need help later

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1or like this: dw:1436026652043:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I will stay here in Open Study, for at least 1 hour

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok:) Thanks I will email you again soon
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.