Systems Of Nonlinear Equations Word Problems Worksheet
Jovanna Ponder
Problem:
Lacy is speeding in her car, and sees a parked police car on the side of the road right next to her at t=0 seconds. She immediately decelerates, but the police car accelerates to catch up with her. (Assume the two cars are going in the same direction in parallel paths).
We need to find the intersection of the two functions, since that is when the distances are the same. Remember that the graphs are not necessarily the paths of the cars, but rather a model of the how far they go given a certain time in seconds.
This is common sense, and is probably familiar to you from your experience with coins and buying things. But notice that these examples tell me what the general equation should be: The number of items times the cost (or value) per item gives the total cost (or value). This is where I get the headings on the tables below.
Be sure you understand why the equations in the pennies and nickels rows are the way they are: The number of coins times the value per coin is the total value. If the words seem too abstract to grasp, try some examples:
3. The total value or total amount will go in the third column. This might be the total cost of a number of tickets, the distance travelled by a car or a plane, the total interest earned by an investment, and so on.
In some cases, you add the numbers in some of the columns in a table. In other cases, you set two of the numbers in a column equal, or subtract one number from another. There is no general rule for telling which of these things to do: You have to think about what the problem is telling you.
Example. An investor buys a total of 360 shares of two stocks. The price of one stock is $35 per share, while the price of the other stock is $45 per share. The investor spends a total of $15000. How many shares of each stock did the investor buy?
Example. Phoebe has some 32-cent stamps, some 29-cent stamps, and some 3-cent stamps. The number of 29-cent stamps is 10 less than the number of 32-cent stamps, while the number of 3-cent stamps is 5 less than the number of 29-cent stamps. The total value of the stamps is $9.45. How many of each stamp does she have?
Example. $6000 is divided between two accounts, one paying interest and the other paying interest. At the end of one interest period, the interest earned by the account exceeds the interest earned by the account by $65. How much was invested in each account?
Example. Bonzo invests some money at interest. He also invests $1700 more than twice that amount at interest. At the end of one interest period, the total interest earned was $278. How much was invested at each rate?
There are various kinds of mixture problems. The first few involve mixtures of different things which cost different amounts per pound. For instance, if you have 4 pounds of candy which costs $2 per pound, the total cost of the candy is
Example. Calvin mixes candy that sells for $2.00 per pound with candy that costs $3.60 per pound to make 50 pounds of candy selling for $2.16 per pound. How many pounds of each kind of candy did he use in the mix?
Example. Phoebe wants to mix raisins worth $1.60 per pounds with nuts worth $2.45 per pound to make 17 pounds of a mixture worth $2 per pound. How many pounds of raisins and how many pounds of nuts should she use?
Other mixture problems involve solutions. For instance, a solution may be acid, or alcohol. What does this mean? Suppose you have 80 gallons of a solution which is acid. Then the number of gallons of (pure) acid in the solution is
Example. Amounts of a alcohol solution and a alcohol solution are to be mixed to produce 24 gallons of a alcohol solution. How many gallons of the alcohol solution and how many gallons of the alcohol solution should be used?
A system can contain as many equations as you can input. Furthermore, it can contain different types of equations. For example, one equation can be linear, and the other can be a nonlinear equation. We will call this system a nonlinear system of equations. In easy words, a system of equations is nonlinear when at least one of its equations is not in the first degree. The condition is that one of the system's equations shouldn't be linear. However, it can have many nonlinear equations but if we talk about the lower limit, the system should have at least one nonlinear equation.
Brief review of arithmetic operations and basic algebraic concepts: factoring, operations with polynomials and rational expressions, linear equations and word problems, graphing linear equations, simplification of expressions involving radicals or negative exponents, and elementary work with quadratic equations. Grades are reported as pass/fail.
Prerequisites: Placement and two units of college-preparatory mathematics; if a student has previously been placed in MATH 005, a passing grade in MATH 005 is required. Intermediate-level course including work on functions, graphs, linear equations and inequalities, quadratic equations, systems of equations, and operations with exponents and radicals. The solution of word problems is stressed. NOT APPLICABLE to UA Core Curriculum mathematics requirement. Grades are reported as A, B, C or NC (No Credit).
This course is intended to give an overview of topics in finite mathematics with applications. This course covers mathematics of finance, logic, set theory, elementary probability and statistics. This course does not provide sufficient background for students who will need to take Precalculus Algebra or Calculus. Prerequisites: Placement and two units of college-preparatory mathematics; if a student has previously been placed in MATH 005, a passing grade in MATH 005 is required.
A higher-level course emphasizing functions including polynomial functions, rational functions, and the exponential and logarithmic functions. Graphs of these functions are stressed. The course also includes work on equations, inequalities, systems of equations, the binomial theorem, and the complex and rational roots of polynomials. Applications are stressed. Grades are reported as A, B, C or NC (No Credit). Degree credit will not be granted for both MATH 115 and (MATH 112 or MATH 113).
Continuation of MATH 112. The course includes study of trigonometric functions, inverse trigonometric functions, trigonometric identities and trigonometric equations. Complex numbers, De Moivre's Theorem, polar coordinates, vectors and other topics in algebra are also addressed, including conic sections, sequences and series. Grades are reported as A, B, C or NC (No Credit). Degree credit will not be granted for both MATH 115 and (MATH 112 or MATH 113).
Properties and graphs of exponential, logarithmic, and trigonometric functions are emphasized. Also includes trigonometric identities, polynomial and rational functions, inequalities, systems of equations, vectors, and polar coordinates. Grades are reported as A, B, C, or NC (No credit). Degree credit will not be granted for both MATH 115 and (MATH 112 or MATH 113).
A brief overview of calculus primarily for students in the Culverhouse College of Commerce and Business Administration. This course does not provide sufficient background for students who will need higher levels of Calculus. Note: This course does not satisfy the requirement for MATH 125 or 126. Degree credit will not be granted for both MATH 121 and MATH 125 or MATH 145.
This is the first of three courses in the basic calculus sequence. Topics include the limit of a function; the derivative of algebraic, trigonometric, exponential, and logarithmic functions; and the definite integral. Applications of the derivative are covered in detail, including approximations of error using differentials, maxima and minima problems, and curve sketching using calculus. There is also a brief review of selected precalculus topics at the beginning of the course. Degree credit will not be granted for both MATH 121 and MATH 125 or MATH 145.
This is the second of three courses in the basic calculus sequence. Topics include vectors and the geometry of space, applications of integration, integration techniques, L'Hopital's Rule, improper integrals, parametric equations, polar coordinates, conic sections and infinite series.
This course covers the same material as MATH 126 but in a depth appropriate for honors students. It is the second course in the three part honors calculus sequence for students majoring in mathematics, science or engineering. Topics include vectors and the geometry of space, L'Hospital's Rule, applications of integration, integration techniques, improper integrals, infinite series, conic sections, plane curves, parametric equations, and polar coordinates.
Properties of two- and three-dimensional shapes, rigid motion transformations, similarity, spatial reasoning, and the process and techniques of measurement. Class activities initiate investigations of underlying mathematical structure in the exploration of shape and space. Emphasis is on the explanation of the mathematical thought process. Technology specifically designed to facilitate geometric explorations is integrated throughout the course.
Data analysis, statistics, and probability, including collecting, displaying/representing, exploring, and interpreting data, probability models, and applications. Focus is on statistics for problem-solving and decision making, rather than calculation. Class activities deepen the understanding of fundamental issues in learning to work with data. Technology specifically designed for data-driven investigations and statistical analysis related to elementary school teaching is integrated throughout the course.
This is the third of three courses in the basic calculus sequence. Topics include: vector functions and motion in space; functions of two or more variables and their partial derivatives; and applications of partial derivatives (including Lagrange multipliers), quadric surfaces, multiple integration (including Jacobian), line integrals, Green's Theorem, vector analysis, surface integrals and Stokes' Theorem.
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