
Concept explainers
a.
To write:
An equation giving the unharvested area y of the larger field (in acres) after x days.
a.

Answer to Problem 31E
The equation y=1000−50x represents the unharvested area y of the larger field (in acres) after x days.
Explanation of Solution
Given:
Two farmers each harvest 50 acres of corn per day from their fields. The area of one farmer’s field is 1000 acres, and the area of the other farmer’s field is 600 acres.
Calculation:
Let x represent number of days and y represent unharvested area.
We have been given that the farmer harvest 50 acres of corn per day from their fields, so number of acres harvested in x days would be 50x .
The unharvested area after xdays would be total area minus area harvested in x days. The larger area is 1000 acres.
y=1000−50x
Therefore, the equation y=1000−50x represents the unharvested areaof the larger field (in acres) after x days.
b.
To write:
An equation giving the unharvested area y of the smaller field (in acres) after x days.
b.

Answer to Problem 31E
The equation y=600−50x represents the unharvested area of the smaller field (in acres) after x days.
Explanation of Solution
Given:
Two farmers each harvest 50 acres of corn per day from their fields. The area of one farmer’s field is 1000 acres, and the area of the other farmer’s field is 600 acres.
Calculation:
Let x represent number of days and y represent unharvested area.
We have been given that the farmer harvest 50 acres of corn per day from their fields, so number of acres harvested in x days would be 50x .
The unharvested area after x days would be total area minus area harvested in x days. The smaller area is 600 acres.
y=1000−50x
Therefore, the equation y=600−50x represents the unharvested area of the smaller field (in acres) after x days.
c.
To graph:
The equations from part (a) and part (b) in the same coordinate plane. Identify the slope and y -intercept of each graph.
c.

Answer to Problem 31E
Our required graph would look like:
Explanation of Solution
Given:
Two farmers each harvest 50 acres of corn per day from their fields. The area of one farmer’s field is 1000 acres, and the area of the other farmer’s field is 600 acres.
Concept used:
The equation of a line in slope-intercept form is y=mx+b , where m represents slope of line and b represents the y -intercept.
Calculation:
Upon comparing equation y=1000−50x with slope-intercept form, we can see that slope is −50 and the y -intercept is 1000.
Upon comparing equation y=600−50x with slope-intercept form, we can see that slope is −50 and the y -intercept is 600.
Upon graphing our both equations on same coordinate plane, we will get our required graph as shown below:
d.
What is the geometric relationship between graphs from part (c)? How do you know?
d.

Answer to Problem 31E
The area under the graph of y=1000−50x is more than the area under the graph of y=600−50x .
Explanation of Solution
Given:
Two farmers each harvest 50 acres of corn per day from their fields. The area of one farmer’s field is 1000 acres, and the area of the other farmer’s field is 600 acres.
Calculation:
Upon looking at our graph in part (c), we can see that the graph of y=1000−50x covers more area than the graph of y=600−50x .
Therefore, the area under the graph of y=1000−50x is more than the area under the graph of y=600−50x .
e.
How long does it take to harvest the corn in the larger field? in the smaller field?
e.

Answer to Problem 31E
It will take 20 days to harvest the corn in the larger field.
It will take 12 days to harvest the corn in the smaller field.
Explanation of Solution
Given:
Two farmers each harvest 50 acres of corn per day from their fields. The area of one farmer’s field is 1000 acres, and the area of the other farmer’s field is 600 acres.
Calculation:
To find the number of days, it will take to harvest the corn in the larger field, we will substitute y=0 in equation y=1000−50x and solve for x as:
y=1000−50x0=1000−50x50x=1000(Adding 50x on both sides)50x50x=100050(Dividing both sides by 50)x=20
Therefore, it will take 20 days to harvest the corn in larger field.
To find the number of days, it will take to harvest the corn in the smaller field, we will substitute y=0 in equation y=600−50x and solve for x as:
y=600−50x0=600−50x50x=600(Adding 50x on both sides)50x50x=60050(Dividing both sides by 50)x=12
Therefore, it will take 12 days to harvest the corn in smaller field.
Chapter 8 Solutions
Pre-Algebra
Additional Math Textbook Solutions
Introductory Statistics
Elementary Statistics (13th Edition)
Elementary Statistics: Picturing the World (7th Edition)
College Algebra with Modeling & Visualization (5th Edition)
Pre-Algebra Student Edition
Calculus: Early Transcendentals (2nd Edition)
- a) [1√2-31x+1√3-11y = x (1 - √2) + √34 LI√2-21x-1√3-3/4= √34 - √2x-4arrow_forwardPlease Help me answer this linear algebra question. This is a practice textbook question.arrow_forward1. a scientist observed a bacterium in a microscope. it measured about .0000029 meter in diameter which of the following is closest to it? A- 2 x 10^-6, B- 2 x 10^-5, C- 3 x 10^-5, or D- 3 x 10^-6 2.express the product of 500 and 400 in scientific notation. is it 2 x 10^5 or 2 x 10^4 or 2 x 10^3 or 20 x 10^4arrow_forward
- Please Help me answer this linear algebra question. This is a practice textbook question.arrow_forwardPlease Help me answer this linear algebra question. This is a practice textbook question.arrow_forwardTY D om E h om ng 00 C B A G F Q ו 3 13 Details Find an Euler path for the graph. Enter your response as a sequence of vertices in the order they are visited, for example, ABCDEA. fic ► Question Help: Video Message instructor Submit Question tor arch 園 A Wind advisoryarrow_forward
- You are provided with three 2D data points, p1, p2 and p3. Solving A C = B for C provides youwith the coefficients of a natural cubic spline curve that interpolates these points.Additionally, you have been given A and B, but some elements are missing. Moreover, the last two rowsof A are entirely absent. Your task is to determine and fill in the missing elements. For the last two rows,enforce a zero tangent at the beginning (in p1) and a not-a-knot boundary condition in p2. The matricesA and B are given as follows:Explain how to find the entries of A and B . How would you adapt these matrices if the data pointswere 3D? What if your spline should go through five data points? How many “extra rows” would there thenbe (with “extra” meaning “in addition to securing C2-continuity”)?arrow_forwardWhich graph represents f(x) = √x-2+3?arrow_forwardPractice Assignment 5.6 Rational Functions M Practice Assig Practice Assignment 5.6 Rational Functions Score: 120/150 Answered: 12/15 Question 10 A Write an equation for the function graphed below 5 + 4 1 2 H + + -7 -6 -5 -4 -3 -2 -1 2 34567 | -2 ర y = Question Help: Video Message instructor Post to forum Submit Questionarrow_forward
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education





