a.
To graph: The data given and the graph the model.
a.

Explanation of Solution
Given:
Following data is given in the form of a table
Year | Bachelor’s degrees, B (in thousands) |
2005 | 826 |
2006 | 855 |
2007 | 875 |
2008 | 895 |
2009 | 916 |
2010 | 943 |
2011 | 982 |
2012 | 1026 |
2013 | 1053 |
2014 | 1068 |
2015 | 1082 |
2016 | 1099 |
The data can be approximated by the linear model
Graph:
By using the above data, points and the model can be plotted as
Interpretation:
The graph shows that the points plotted are very close to the graph of the linear model.
b.
To find: the bachelor’s degrees earned by women for each year from 2005 through 2016 by the linear model.
b.

Explanation of Solution
Given:
The linear model
Calculation:
Table below shows the data for each year from 2005 to 2016.
Year | Bachelor’s degrees, B (in thousands) |
2005 | 823 |
2006 | 849.42 |
2007 | 875.84 |
2008 | 902.26 |
2009 | 928.68 |
2010 | 955.1 |
2011 | 981.52 |
2012 | 1007.94 |
2013 | 1034.36 |
2014 | 1060.78 |
2015 | 1087.2 |
2016 | 1113.62 |
c.
To compare: the given data with the data obtained from linear model.
c.

Explanation of Solution
Given:
Following data is given in the form of a table
Year | Bachelor’s degrees, B (in thousands) |
2005 | 826 |
2006 | 855 |
2007 | 875 |
2008 | 895 |
2009 | 916 |
2010 | 943 |
2011 | 982 |
2012 | 1026 |
2013 | 1053 |
2014 | 1068 |
2015 | 1082 |
2016 | 1099 |
The data can be approximated by the linear model
Calculation:
Year | Bachelor’s degrees, B (in thousands)
(data given) | Bachelor’s degrees, B (in thousands)
(data from the linear model ) | Difference between the two values |
2005 | 826 | 823 | 3 |
2006 | 855 | 849.42 | 5.58 |
2007 | 875 | 875.84 | -0.84 |
2008 | 895 | 902.26 | -7.62 |
2009 | 916 | 928.68 | -12.68 |
2010 | 943 | 955.1 | -12.1 |
2011 | 982 | 981.52 | 0.48 |
2012 | 1026 | 1007.94 | 18.06 |
2013 | 1053 | 1034.36 | 18.64 |
2014 | 1068 | 1060.78 | 7.22 |
2015 | 1082 | 1087.2 | -5.2 |
2016 | 1099 | 1113.62 | -14.62 |
As can be seen from the table, the difference between the given data and the data obtained from the linear model is very less thus; the model is best suited for the data.
d.
To find: the slope and the y -intercept of the model.
d.

Explanation of Solution
Given:
The linear model:
Concept used; The equation of a straight line is given by
Calculation:
We have the equation of linear model as
Thus the slope of the model is,
Slope tells how much the value of y changes with the change in x .
The y -intercept of the linear model shows the value at t = 0, as we know t = 5 corresponds to 2005, t = 0 will correspond to 2000. Thus the y -intercept gives the number of bachelor’s degrees earned by women in the year 2000.
e.
To find: the number of bachelor’s degrees earned by women in the year 2022
e.

Explanation of Solution
Given:
The linear model
Calculation:
t = 5 corresponds to 2005, therefore 2022 is given by t = 22,
Putting the value of t as 22 in the linear model we get,
Therefore, the number of bachelor’s degrees earned by women in the year 2022 is 1272.14 thousands
Chapter 1 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
- Please as many detarrow_forward8–23. Sketching vector fields Sketch the following vector fieldsarrow_forward25-30. Normal and tangential components For the vector field F and curve C, complete the following: a. Determine the points (if any) along the curve C at which the vector field F is tangent to C. b. Determine the points (if any) along the curve C at which the vector field F is normal to C. c. Sketch C and a few representative vectors of F on C. 25. F = (2½³, 0); c = {(x, y); y − x² = 1} 26. F = x (23 - 212) ; C = {(x, y); y = x² = 1}) , 2 27. F(x, y); C = {(x, y): x² + y² = 4} 28. F = (y, x); C = {(x, y): x² + y² = 1} 29. F = (x, y); C = 30. F = (y, x); C = {(x, y): x = 1} {(x, y): x² + y² = 1}arrow_forward
- ٣/١ B msl kd 180 Ka, Sin (1) I sin () sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 x 50 G 5005 1000 s = 1000-950 Copper bosses 5kW Rotor input 5 0.05 : loo kw 6) 1 /0001 ined sove in peaper I need a detailed solution on paper please وه اذا ميريد شرح الكتب فقط ١٥٠ DC 7) rotor a ' (y+xlny + xe*)dx + (xsiny + xlnx + dy = 0. Q1// Find the solution of: ( 357arrow_forward۳/۱ R₂ = X2 2) slots per pole per phase 3/31 B. 180 msl Kas Sin (I) 1sin() sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30): 0.866 4) Rotating 5) Synchronous speeds 120×50 looo G 1000-950 1000 Copper losses 5kw Rotor input 5 loo kw 0.05 6) 1 اذا ميريد شرح الكتب فقط look 7) rotor DC ined sove in peaper I need a detailed solution on paper please 0 64 Find the general solution of the following equations: QI//y(4)-16y= 0. Find the general solution of the following equations: Q2ll yll-4y/ +13y=esinx.arrow_forwardR₂ = X2 2) slots per pole per phase = 3/31 B-180 60 msl kd Kas Sin () 2 I sin (6) sin(30) Sin (30) اذا مريد شرح الكتب بس 0 بالفراغ 3 Cos (30) 0.866 4) Rotating ined sove in peaper 5) Synchronous speed s 120×50 6 s = 1000-950 1000 Copper losses 5kw Rotor input 5 0.05 6) 1 loo kw اذا ميريد شرح الكتب فقط Look 7) rotov DC I need a detailed solution on paper please 0 64 Solve the following equations: 0 Q1// Find the solution of: ( y • with y(0) = 1. dx x²+y²arrow_forward
- R₂ = X2 2) slots per pole per phase = 3/3 1 B-180-60 msl Ka Sin (1) Isin () sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 x 50 s = 1000-950 1000 Copper losses 5kw Rotor input 5 6) 1 0.05 G 50105 loo kw اذا ميريد شرح الكتب فقط look 7) rotov DC ined sove in peaper I need a detailed solution on paper please 064 2- A hot ball (D=15 cm ) is cooled by forced air T.-30°C, the rate of heat transfer from the ball is 460.86 W. Take for the air -0.025 Wim °C and Nu=144.89, find the ball surface temperature a) 300 °C 16 b) 327 °C c) 376 °C d) None か = 750 01arrow_forwardDon't do 14. Please solve 19arrow_forwardPlease solve 14 and 15arrow_forward
- 1. Consider the following system of equations: x13x2 + 4x3 - 5x4 = 7 -2x13x2 + x3 - 6x4 = 7 x16x213x3 - 21x4 = 28 a) Solve the system. Write your solution in parametric and vector form. b) What is a geometric description of the solution. 7 c) Is v = 7 in the span of the set S= [28. 1 HE 3 -5 3 ·6 ? If it is, write v 6 as a linear combination of the vectors in S. Justify. d) How many solutions are there to the associated homogeneous system for the system above? Justify. e) Let A be the coefficient matrix from the system above. Find the set of all solutions to Ax = 0. f) Is there a solution to Ax=b for all b in R³? Justify.arrow_forward4. Suppose that A is made up of 5 column vectors in R³, and suppose that the rank(A)=3. a. How many solutions are there to Ax=0? Justify. b. What is a geometric description for the nullspace(A)? Justify. c. Do the column vectors of A span R³? Justify. d. Is A invertible? Justify.arrow_forward3. Suppose that A is 5 x 5 and rank(A)=4. Use this information to answer the following. a. Give a geometric description of nullspace(A). Justify. b. Is A invertible? Justify. c. Give a geometric description of the span of the column vectors of A. What space are the column vectors of A in? Justify. d. What is determinant of A? Justify.arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning





