2.7 NONLINEAR INEQUALITIES Objectives Solve polynomial inequalities. Solve rational inequalities. Use inequalities to model and solve real-life problems. *We have discussed polynomial and rational functions and equations. Now, we will discuss inequalities that contain polynomial and rational functions. Polynomial Inequalities *This entire section hinges upon the fact that a real number can only be one of three things: positive, ___________________ , or ___________________ . This is called the Law of Trichotomy.
*If an expression contains division (such as
1 ), then (depending on x ) that expression could be: x
positive, ___________________ , ______________________ , or __________________________ .
*What are key numbers (critical values) of a polynomial inequality? How do they help determine the solution set of a polynomial inequality?
TURN OVER
Ex) Solve the following polynomial inequality and show on the x − axis which x − values are in the solution set.
x2 − x − 6 < 0
*How does the graph of y = x 2 − x − 6 relate to the above example? Sketch the graph using a graphing utility to help.
NEXT PAGE
Ex) Solve the following polynomial inequality and show on the x − axis which x − values are in the solution set.
2 x 3 − 3 x 2 − 32 x > −48
TURN OVER
Rational Inequalities *Solving rational inequalities is not that different than solving polynomial inequalities. The only difference is that one more type of key number (critical value) must be considered. *In general, how are the key numbers of a rational inequality determined?
Ex) Solve the following rational inequality and show on the x − axis which x − values are in the solution set.
2x − 7 ≤3 x −5
NEXT PAGE
Applications Ex) The marketing department of a calculator manufacturer has determined that the demand for a new model of calculator is
p= 100 − 0.00001x, 0 ≤ x ≤ 10, 000, 000 where p is the price per calculator (in dollars) and x represents the number of calculators sold. The total cost of producing x calculators is
= C 10 x + 2,500, 00. What prices can the company charge per calculator to obtain a profit of at least $190, 000, 000?
Use inequalities to model and solve real-life problems. *We have discussed ... Ex) Solve the following polynomial inequality and show on the x â axis which x â values are in the solution. set. 3 2 2 3 32 48 xx x â â >â. TURN OVER. Page 3 of 6. 2.7 Nonlinear Inequalities.pdf. 2.7 Nonlinear Inequalities.pdf. Open. Extract.
Aug 5, 2004 - H. - _- o 0o0. 2 1 ..|4. 03:5'. 6 0. o a. Mn. 0m 8. Me. 0m T. n n b. 50 1| - 4.I. FIG. 26. FIG. 1C .... The seismic waves are detected at or near the surface by seismic receivers. .... 13 illustrates a shift register of degree 4 With fe
Reactive planners improvise solutions at run time as uncertainties, predicted or unpredicted, arise. A conditional plan does not exhibit the 'persistent goal- ..... 4) The contexts for the goals in the plan form a tautol- ogy. The context of every po
system theory is not much beyond the typical third- or fourth-year undergraduate course ... Use of this material for business or commercial purposes is prohibited. .... A system represented by (5) will be called a degree-n homogeneous system.
Nov 27, 2016 - Life Center C200. Church Office. If you have a need or question, please call the church office, 919-467-9394, or email [email protected]. Office.
noisy speech, these two operations lead to some degrada- tion in recognition performance for clean speech. In this paper, we try to alleviate this problem, first by introducing the energy information back into the PAC based features, and second by st
E.M. LYON. BP 174 ... College and the London Business School). The data .... PDF. 27.PDF. Open. Extract. Open with. Sign In. Main menu. Displaying 27.PDF.
Whoops! There was a problem loading more pages. Whoops! There was a problem previewing this document. Retrying... Download. Connect more apps... Try one of the apps below to open or edit this item. SEGNATURA_1511170818_Sciope 27 novembre2017ro.pdf. S
Page 1 of 4. Circular No. 27/01/2018-GST. F. No. 354/107/2017-TRU. Government of India. Ministry of Finance. Department of Revenue. Tax research Unit. ****. North Block, New Delhi. 04th January 2018. To,. The Principal Chief Commissioners/ Chief Comm
Anahtar Sözcükler: Nesnelerin Interneti, IoT, Makine-Makine baÄlantı, M2M, ... Abstract: In this paper, I will try to analyse and explain the term âInternet of Thingsâ, ...
May 9, 2017 - Proof of adequate medical screenings to exclude ... improvement of skills of all the organization's personnel engaged in delivery of hospice.
Nov 27, 2016 - you check in on Facebook to White Plains a donation ... Please sign the attendance book in your row, so we might have an ... Page C. Long .... help with: set-up and take-down crews, A.M and P.M. van drivers, meal pro- viders ...
On 3rd May, we will have an opportunity to show that, far from ... moment in which we have to persevere for what is right. In intro- .... woman, who claimed that she was cured of a brain. aneurysm after a photograph of Pope John Paul II spoke to her.
May 9, 2017 - decision for the individual granting the power. (6) Agency. A Home .... availability shall include, but not be limited to, availability by telephone.
May 9, 2017 - (e) Management agreements are generally not changes of ownership if the owner ..... The objectives of those responsible for the performance.
Page. 1. /. 1. Loading⦠Page 1 of 1. Page 1 of 1. 27-48BIROSAWS.pdf. 27-48BIROSAWS.pdf. Open. Extract. Open with. Sign In. Main menu. Displaying 27-48BIROSAWS.pdf.
May 14, 2017 - (4) Degree: A two-year associate degree conferred on students by an eligible postsecondary institution. .... (c) Social Security Number,.
NONTRADITIONAL SCHEDULING: A SMALL BUSINESS PERSPECTIVE ... approaches to nontraditional scheduling are presented, both full-time and part-time options. .... can be maintained via phone, written memos, or computer access.
There was a problem previewing this document. Retrying... Download. Connect more apps... Try one of the apps below to open or edit this item. 27.PISA2012MathReleasedItems.pdf. 27.PISA2012MathReleasedItems.pdf. Open. Extract. Open with. Sign In. Main
Page 1 of 6. CHESTERFIELD COUNTY PUBLIC SCHOOLS. CHESTERFIELD, VIRGINIA. TO: Dr. James F. Lane. Superintendent. FROM: Nita Mensia-Joseph. Chief Operations Officer. DATE: October 7, 2016. SUBJECT: White Paper Related to Manchester Middle School Renova
