Mathematics For Elementary Teachers With Activities
5th Edition
ISBN: 9780134423401
Author: Sybilla Beckmann
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 12.3, Problem 13P
Given that the rectangle ABCD in Figure 12.41 has area 108 square units, determine the area of the shaded triangle. Explain your reasoning
Figure 12.41 Determining the area of the shaded triangle.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
8d6 عدد انباء
Q/ Design a rectangular foo
A
ing of B-2.75m to support a column of
dimensions (0.46 x 0.46) m, dead load =1300kN, live load = 1300kN,
qa-210kPa, fc' 21 MPa, fy- 400 MPa.
=
5 of 5
(i) Let a discrete sample space be given by
Ω = {ω1, 2, 3, 4},
Total marks 12
and let a probability measure P on be given by
P(w1) 0.2, P(w2) = 0.2, P(w3) = 0.5, P(w4) = 0.1.
=
Consider the random variables X1, X2 → R defined by
X₁(w3) = 1, X₁(4) = 1,
X₁(w₁) = 1, X₁(w2) = 2,
X2(w1) = 2, X2(w2) = 2, X2(W3) = 1, X2(w4) = 2.
Find the joint distribution of X1, X2.
(ii)
[4 Marks]
Let Y, Z be random variables on a probability space (N, F, P).
Let the random vector (Y, Z) take on values in the set [0,1] × [0,2] and let the
joint distribution of Y, Z on [0,1] × [0,2] be given by
1
dPy,z(y, z)
(y²z + y²²) dy dz.
Find the distribution Py of the random variable Y.
[8 Marks]
Refer to page 40 for solving a time-optimal control problem.
Instructions:
• Formulate the problem by minimizing the time to reach a target state.
•
Apply Pontryagin's Maximum Principle to derive the optimal control and switching conditions.
• Solve explicitly for the control and state trajectories. Include clear diagrams to visualize the
solution.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing]
Chapter 12 Solutions
Mathematics For Elementary Teachers With Activities
Ch. 12.1 - You have a 5-foot-by-7-foot rectangular rug in...Ch. 12.1 - Draw a 3-cm-by-7-cm rectangle. Then discuss the...Ch. 12.1 - a. Explain how to decompose the large rectangle in...Ch. 12.1 - a. Explain how to decompose the large rectangle in...Ch. 12.1 - Draw a (fairly long) line segment and designate it...Ch. 12.2 - Make a shape that has area 25in2 but that has no...Ch. 12.2 - Flgure 12.14 shows the floor plan for a one-story...Ch. 12.2 - An area problem: The Johnsons are planning to...Ch. 12.2 - Figure 12.15 shows a design for an herb garden,...Ch. 12.2 - Figure 12.16 [g shows the floor plan for a modern,...
Ch. 12.2 - Use the moving and additivity principles to...Ch. 12.2 - Use the moving and additivity principles to...Ch. 12.3 - Use the moving and additivity principles to...Ch. 12.3 - For each triangle in Figure 12.31 , show the...Ch. 12.3 - Use a ruler and compass to draw three identical...Ch. 12.3 - Explain clearly in your own words why the...Ch. 12.3 - Explain clearly in your own words why the...Ch. 12.3 - Becky was asked to divide a rectangle into 4 equal...Ch. 12.3 - Explain how to use the additivity principle to...Ch. 12.3 - Determine the area of the shaded triangle that is...Ch. 12.3 - Determine the area of the shaded shape in Figure...Ch. 12.3 - Determine the area of the shaded triangle in...Ch. 12.3 - Determine the area of the shaded shape in Figure...Ch. 12.3 - Determine the area of the shaded shape in Figure...Ch. 12.3 - Given that the rectangle ABCD in Figure 12.41 has...Ch. 12.4 - Josie has two wooden beams that are 15 feet long...Ch. 12.4 - Figure 12.47 shows a shaded parallelogram inside a...Ch. 12.4 - In the text, we saw a way to explain why the area...Ch. 12.4 - Figure 12.49 shows a trapezoid. This problem will...Ch. 12.4 - Use the moving and additivity principles to...Ch. 12.4 - Find a formula for the area of a rhombus (see...Ch. 12.4 - Determine the areas (in square units) of the 4...Ch. 12.4 - Determine the area (in square units) of the...Ch. 12.4 - Determine the area of the shaded shapes in Figure...Ch. 12.4 - A rug company weaves rugs that are made by...Ch. 12.4 - Determine the area of the shaded region in Figure...Ch. 12.4 - Given that the shaded shape in Figure 12.58 is a...Ch. 12.4 - Figure 12.59 shows a map of some land. Determine...Ch. 12.5 - Figure 12.68 shows a triangle on a pegboard....Ch. 12.5 - Make a drawing to show the result of shearing the...Ch. 12.5 - Prob. 3PCh. 12.5 - Make a drawing to show the result of shearing the...Ch. 12.5 - a. Make a drawing to show the result of shearing...Ch. 12.5 - The boundary between the Johnson and the Zhang...Ch. 12.5 - Suppose that in a trapezoid ABCD, as in Figure...Ch. 12.5 - Prob. 8PCh. 12.6 - In your own words. discuss how the diameter and...Ch. 12.6 - Tim works on the following exercise: For each...Ch. 12.6 - A large running track is constructed to have...Ch. 12.6 - Suppose you have a large spool used for winding...Ch. 12.6 - Suppose that when pizza dough is rolled out it...Ch. 12.6 - Lauriann and Kinsey are in charge of the annual...Ch. 12.6 - Penguins huddle together to stay warm in very cold...Ch. 12.6 - Jack has a truck that requires tires that are 26...Ch. 12.6 - Let r units denote the radius of each circle in...Ch. 12.7 - Suppose that you have a map on which 1 inch...Ch. 12.7 - Suppose that you have a map on which 1 inch...Ch. 12.7 - Suppose that you have a map on which 1 inch...Ch. 12.8 - Suppose that a student in your class wants to know...Ch. 12.8 - Sarah is confused about the difference between the...Ch. 12.8 - Describe a concrete way to demonstrate that many...Ch. 12.8 - Anya wants to draw many different rectangles that...Ch. 12.8 - On graph paper, draw 4 different rectangles that...Ch. 12.8 - Which of the lengths that follow could be the...Ch. 12.8 - a. Without using a calculator, fund the lengths...Ch. 12.8 - Draw 4 different rectangles, all of which have a...Ch. 12.8 - Draw 4 different rectangles, all of which have...Ch. 12.8 - A forest has a perimeter of 210 mi, but no...Ch. 12.8 - Bob wants to find the area of an irregular shape....Ch. 12.8 - Consider all rectangles whose area is 4 in2 ,...Ch. 12.9 - Jessica says she doesn‘t understand the...Ch. 12.9 - Town B is 380 km due south of town A. Town C is...Ch. 12.9 - What length ribbon will you need to stretch from...Ch. 12.9 - Rover the dog is on a 30-foot leash. One end of...Ch. 12.9 - Carmina and Antone measure that the distance...Ch. 12.9 - Use the Pythagorean theorem to help you determine...Ch. 12.9 - Assuming that the earth is a perfectly round,...
Additional Math Textbook Solutions
Find more solutions based on key concepts
1. How much money is Joe earning when he’s 30?
Pathways To Math Literacy (looseleaf)
Find E(X) for each of the distributions given in Exercise 2.1-3.
Probability And Statistical Inference (10th Edition)
Empirical versus Theoretical A Monopoly player claims that the probability of getting a 4 when rolling a six-si...
Introductory Statistics
In Exercises 9-20, use the data in the following table, which lists drive-thru order accuracy at popular fast f...
Elementary Statistics (13th Edition)
NOTE: Write your answers using interval notation when appropriate.
CHECKING ANALYTIC SKILLS Fill in each blank ...
Graphical Approach To College Algebra
1. How is a sample related to a population?
Elementary Statistics: Picturing the World (7th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Q1/ Two plate load tests were conducted in a C-0 soil as given belo Determine the required size of a footing to carry a load of 1250 kN for the same settlement of 30 mm. Size of plates (m) Load (KN) Settlement (mm) 0.3 x 0.3 40 30 0.6 x 0.6 100 30 Qx 0.6zarrow_forwardTotal marks 16 5. Let (,,P) be a probability space and let X : → R be a random variable whose probability density function is given by f(x) = }}|x|e¯|×| for x Є R. (i) (ii) Find the characteristic function of the random variable X. [8 Marks] Using the result of (i), calculate the first two moments of the random variable X, i.e., E(X") for n = 1, 2. (iii) What is the variance of X? [6 Marks] [2 Marks]arrow_forwardRefer to page 12 for a problem on solving a homogeneous differential equation. Instructions: • Simplify the equation into a homogeneous form. Use appropriate substitutions to reduce complexity. Solve systematically and verify the final result with clear back-substitutions. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]arrow_forward
- Refer to page 36 for solving a bang-bang control problem. Instructions: • Formulate the problem, identifying the control constraints. • • Apply Pontryagin's Maximum Principle to derive the switching conditions. Clearly illustrate the switching points in the control trajectory. Verify the solution satisfies the optimality criteria. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing]arrow_forwardTotal marks 16 5. Let (N,F,P) be a probability space and let X : N → R be a random variable such that the probability density function is given by f(x)=ex for x € R. (i) Find the characteristic function of the random variable X. [8 Marks] (ii) Using the result of (i), calculate the first two moments of the random variable X, i.e., E(X") for n = 1,2. (iii) What is the variance of X. [6 Marks] [2 Marks]arrow_forward6. Let P be the standard normal distribution, i.e., P is the proba- bility measure on (R, B(R)) given by 1 dP(x) = 를 = e dx. √2πT Consider the random variables 21 fn(x) = (1 + x²) en+2, x Є R, n Є N. Using the dominated convergence theorem, prove that the limit Total marks 9 exists and find it. lim E(fn) n∞ [9 Marks]arrow_forward
- Refer to page 38 for solving an optimal control problem using dynamic programming. Instructions: • Define the value function and derive the Hamilton-Jacobi-Bellman (HJB) equation. • Solve the HJB equation explicitly, showing all intermediate steps and justifications. Verify the solution satisfies the boundary conditions and optimality. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]arrow_forwardRefer to page 18 for solving a second-order linear non-homogeneous differential equation. Instructions: Solve the associated homogeneous equation first. Use either the method of undetermined coefficients or variation of parameters for the particular solution. • Provide detailed steps for combining solutions into the general solution. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing]arrow_forward6. Let X be a random variable taking values in (0,∞) with proba- bility density function fx(u) = 5e5u u > 0. Total marks 8 Let Y = X2. Find the probability density function of Y. [8 Marks]arrow_forward
- 5. Let a probability measure P on ([0,3], B([0,3])) be given by 1 dP(s): = ½ s² ds. 9 Consider a random variable X : [0,3] → R given by X(s) = s², sc [0,3]. S Total marks 7 Find the distribution of X. [7 Marks]arrow_forwardRefer to page 24 for solving a differential equation using Laplace transforms. Instructions: Take the Laplace transform of the given equation, applying initial conditions appropriately. ⚫ Solve the resulting algebraic equation and find the inverse transform. Provide step-by-step solutions with intermediate results and final verification. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing]arrow_forwardRefer to page 30 for deriving the Euler-Lagrange equation for an optimal control problem. Instructions: • Use the calculus of variations to derive the Euler-Lagrange equation. Clearly define the functional being minimized or maximized. Provide step-by-step derivations, including all necessary boundary conditions. Avoid skipping critical explanations. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
An Introduction to Area | Teaching Maths | EasyTeaching; Author: EasyTeaching;https://www.youtube.com/watch?v=_uKKl8R1xBM;License: Standard YouTube License, CC-BY
Area of a Rectangle, Triangle, Circle & Sector, Trapezoid, Square, Parallelogram, Rhombus, Geometry; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=JnLDmw3bbuw;License: Standard YouTube License, CC-BY