(a)
The list of all the numbers between 1 and 2.
(a)
Answer to Problem 14CE
There are infinite numbers between 1 and 2.
Explanation of Solution
Given information:
The graph is shown below as,
Formula used:
The rational and irrational numbers.
Calculation:
List all numbers between 1 and 2.
From the referred figure observe that,
There are infinite numbers between two numbers and on a number line every point is paired with a number and every number is paired with a point.
Because between any two number there are infinite rational and irrational numbers.
Therefore, from the above argument:
There are infinite numbers between 1 and 2.
Conclusion:
There are infinite numbers between 1 and 2.
(b)
To find: The point on the number line for every number between 1 and 2.
(b)
Answer to Problem 14CE
A point on the number line for every number between 1 and 2 is possible.
Explanation of Solution
Given information:
The graph is shown below as,
Formula used:
The rational and irrational numbers.
Calculation:
Find a point on the number line for every number between 1 and 2 if possible.
There are infinite numbers between two numbers and on a number line every point is paired with a number and every number is paired with a point.
Because between any two number there are infinite rational and irrational numbers.
Therefore from the above argument, it is clear that a point on the number line for every number between 1 and 2 is possible.
Conclusion:
A point on the number line for every number between 1 and 2 is possible.
(c)
The number of points between S and T.
(c)
Answer to Problem 14CE
All the numbers between 1 and 2 are moving towards 2, thus numbers between 1 and 2 cannot be greater than 2.
Explanation of Solution
Given information:
The graph is shown below as,
Formula used:
The infinite rational and irrational numbers are used.
Calculation:
Find the limit to the number of points between S and T if possible.
Because between any two numbers there are infinite rational and irrational numbers and the numbers are in increasing order.
All the numbers between 1 and 2 are moving towards 2, thus numbers between 1 and 2 cannot be greater than 2.
Conclusion:
All the numbers between 1 and 2 are moving towards 2, thus numbers between 1 and 2 cannot be greater than 2.
Chapter 1 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (4th Edition)
Introductory Statistics
Elementary Statistics (13th Edition)
College Algebra (7th Edition)
Algebra and Trigonometry (6th Edition)
College Algebra with Modeling & Visualization (5th Edition)
- 3. Construct a triangle in the Poincare plane with all sides equal to ln(2). (Hint: Use the fact that, the circle with center (0,a) and radius ln(r), r>1 in the Poincaré plane is equal to the point set { (x,y) : x^2+(y-1/2(r+1/r)a)^2=1/4(r-1/r)^2a^2 }arrow_forwardn. g. = neutral geometry <ABC = angle ABC \leq = less or equal than sqrt{x} = square root of x cLr = the line in the Poincaré plane defined by the equation (x-c)^2+y^2=r^2 1. Find the bisector of the angle <ABC in the Poincaré plane, where A=(0,5), B=(0,3) and C=(2,\sqrt{21})arrow_forward2. Let l=2L\sqrt{5} and P=(1,2) in the Poincaré plane. Find the uniqe line l' through P such that l' is orthogonal to l.arrow_forward
- Let A, B and C be three points in neutral geometry, lying on a circle with center D. If D is in the interior of the triangle ABC, then show that m(<ABC) \leq 1/2m(<ADC).arrow_forwardиз Review the deck below and determine its total square footage (add its deck and backsplash square footage together to get the result). Type your answer in the entry box and click Submit. 126 1/2" 5" backsplash A 158" CL 79" B 26" Type your answer here.arrow_forwardIn the graph below triangle I'J'K' is the image of triangle UK after a dilation. 104Y 9 CO 8 7 6 5 I 4 3 2 J -10 -9 -8 -7 -6 -5 -4 -3 -21 1 2 3 4 5 6 7 8 9 10 2 K -3 -4 K' 5 -6 What is the center of dilation? (0.0) (-5. 2) (-8. 11 (9.-3) 6- 10arrow_forward
- Select all that apply. 104 8 6 4 2 U U' -10 -8 -6 4 -2 2 4 6 10 -2 V' W' -4 -6 -8 -10 W V Select 2 correct answerts! The side lengths are equal in measure. The scale factor is 1/5. The figure has been enlarged in size. The center of dilation is (0.0) 8 10 Xarrow_forwardIn the graph below triangle I'J'K' is the image of triangle UK after a dilation. 104Y 9 CO 8 7 6 5 I 4 3 2 J -10 -9 -8 -7 -6 -5 -4 -3 -21 1 2 3 4 5 6 7 8 9 10 2 K -3 -4 K' 5 -6 What is the center of dilation? (0.0) (-5. 2) (-8. 11 (9.-3) 6- 10arrow_forwardQll consider the problem -abu+bou+cu=f., u=0 ondor I prove atu, ul conts. @ if Blu,v) = (b. 14, U) + ((4,0) prove that B244) = ((c- — ob)4;4) ③if c±vbo prove that acuius v. elliptic.arrow_forward
- Q3: Define the linear functional J: H₁(2) R by ¡(v) = a(v, v) - L(v) Л Let u be the unique weak solution to a(u,v) = L(v) in H(2) and suppose that a(...) is a symmetric bilinear form on H(2) prove that 1- u is minimizer. 2- u is unique. 3- The minimizer J(u) can be rewritten under 1(u) = u Au-ub, algebraic form 1 2 Where A, b are repictively the stiffence matrix and the load vector Q4: A) Answer 1- show that the solution to -Au = f in A, u = 0 on a satisfies the stability Vullfll and show that ||V(u u)||||||2 - ||vu||2 2- Prove that Where lu-ul Chuz - !ull = a(u, u) = Vu. Vu dx + fu. uds B) Consider the bilinea forta Л a(u, v) = (Au, Av) (Vu, Vv + (Vu, v) + (u,v) Show that a(u, v) continues and V- elliptic on H(2)arrow_forward7) In the diagram below of quadrilateral ABCD, E and F are points on AB and CD respectively, BE=DF, and AE = CF. Which conclusion can be proven? A 1) ED = FB 2) AB CD 3) ZA = ZC 4) ZAED/CFB E B D 0arrow_forward1) In parallelogram EFGH, diagonals EG and FH intersect at point I such that EI = 2x - 2 and EG = 3x + 11. Which of the following is the length of GH? a) 15 b) 28 c) 32 d) 56arrow_forward
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning