HEART OF MATHEMATICS
4th Edition
ISBN: 9781119760061
Author: Burger
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Question
Chapter 4.7, Problem 15MS
To determine
To find: The maximum distance between vertices on a 3 dimensional cube, on a 4 dimensional cube, 5 dimensional cube and in
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Please solving problem2
Problem1
We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. (This model is the same as in Prob. 1 of HW#2).We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.
Please ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.
This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one.
A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The
wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture.
A
B
A
B
at some instant, the piston will be tangent to the circle
(a) Express the x and y coordinates of point A as functions of t:
x= 2 cos(3πt)
and y= 2 sin(3t)
(b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds:
-cot(3πt)
sin(3лt)
(c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +411-
4
-2 sin (3лt)
(d)…
Chapter 4 Solutions
HEART OF MATHEMATICS
Ch. 4.1 - The main event. State the Pythagorean Theorem.Ch. 4.1 - Two out of three. If a right triangle has legs of...Ch. 4.1 - Hypotenuse hype. If a right triangle has legs of...Ch. 4.1 - Assesing area. Suppose you know the base of a...Ch. 4.1 - Squares all around. How does the figure below...Ch. 4.1 - Operating on the triangle. Using a straightedge,...Ch. 4.1 - Excite your friends about right triangles....Ch. 4.1 - Easy as 1,2,3? Can there be a right triangle with...Ch. 4.1 - Sky high (S). On a sunny, warm day, a student...Ch. 4.1 - Sand masting (H). The sailboat named Sand Bug has...
Ch. 4.1 - Getting a pole on a bus. For his 13th birthday,...Ch. 4.1 - The Scarecrow (ExH). In the 1939 movie The Wizard...Ch. 4.1 - Rooting through a spiral. Start with a right...Ch. 4.1 - Is it right? (H) Suppose someone tells you that...Ch. 4.1 - Tfrain trouble (H). Train tracks are made of...Ch. 4.1 - Does everyone have what it takes to be a triangle?...Ch. 4.1 - Getting squared away. In our proof of the...Ch. 4.1 - The practical side of Pythagoras. Suppose you are...Ch. 4.1 - Pythagorean pizzas (H). You have a choice at the...Ch. 4.1 - Natural right (S). Suppose r and s are any two...Ch. 4.1 - Well-rounded shapes. Suppose we have two circles...Ch. 4.1 - A Pythagorean Theorem for triangles other than...Ch. 4.1 - With a group of folks. In a small group, discuss...Ch. 4.1 - Double trouble. Suppose you know a right triangle...Ch. 4.1 - K-ple trouble. Suppose you have a right triangle...Ch. 4.1 - Padding around. You have a rectangular patio with...Ch. 4.1 - Pythagoras goes the distance. Plot the points (5,...Ch. 4.1 - Ahoy there! (H) Your exotic sailboat, which you...Ch. 4.2 - Standing guard. Draw the floor plan of a gallery...Ch. 4.2 - Art appreciation. State the Art Gallery Theorem.Ch. 4.2 - Upping the ante. How many guards do you need for a...Ch. 4.2 - Keep it safe. At what vertices would you place...Ch. 4.2 - Puttoing guards in their place. For each floor...Ch. 4.2 - Guarding the Guggenheim. The Art Gallery Theorem...Ch. 4.2 - TriangulatIng the Louvre (H). Triangulate the...Ch. 4.2 - Triangulating the Clark. Triangulate the floor...Ch. 4.2 - Tricolor me (ExH). For each triangulation, color...Ch. 4.2 - Tricolor hue. For each triangulation, color the...Ch. 4.2 - One-third. Write the number 6 as a sum of three...Ch. 4.2 - Easy watch. Draw a floor plan of a museum with six...Ch. 4.2 - Two watches (S). Draw the floor plan of a museum...Ch. 4.2 - Mirror, mirror on the wall. Consider the floor...Ch. 4.2 - Nine needs three (H). Draw a floor plan for a...Ch. 4.2 - One-third again (ExH). If a natural number is...Ch. 4.2 - Square museum (S). If a museum has only...Ch. 4.2 - Worst squares (H). Draw examples of museums with...Ch. 4.2 - Pie are squared. The circumference of a circle of...Ch. 4.2 - I can see the light. Suppose you are in a...Ch. 4.2 - Less than. Youve tnangulated your polygon and...Ch. 4.2 - Greater than. Youve triangulated your polygon and...Ch. 4.2 - Counting the colors. Your polygon has 40 vertices....Ch. 4.2 - Only red. Twelve of your polygons vertices have...Ch. 4.2 - Totaling triangles. If a polygon has n sides, it...Ch. 4.3 - Defining gold. Explain what makes a rectangle a...Ch. 4.3 - Approximating gold. Which of these numbers is...Ch. 4.3 - Approximating again. Which of the following...Ch. 4.3 - Same solution. Why does the equation l1=1l have...Ch. 4.3 - X marks the unkonw (ExH). Solve eachh equation for...Ch. 4.3 - A cold tall one? Can a Golden Rectangle have a...Ch. 4.3 - Fold the gold (H). Suppose you have a Golden...Ch. 4.3 - Sheets of gold. Suppose you have two sheets of...Ch. 4.3 - Circular logic? (H). Take a Golden Rectangle and...Ch. 4.3 - Growing gold (H). Take a Golden Rectangle and...Ch. 4.3 - Counterfeit gold? Draw a rectangle with its longer...Ch. 4.3 - In the grid (S). Consider the 1010 grid at left....Ch. 4.3 - A nest of gold. Consider the figure of infinitely...Ch. 4.3 - Comparing areas (ExH). Let G be a Golden Rectangle...Ch. 4.3 - Do we get gold? Lets make a rectangle somewhat...Ch. 4.3 - Do we get gold this time? (S) We now describe...Ch. 4.3 - A silver lining? (H) Consider the diagonal in the...Ch. 4.3 - Prob. 20MSCh. 4.3 - Going platinum. Determine the dimensions of a...Ch. 4.3 - Golden triangles. Draw a right triangle with one...Ch. 4.3 - Prob. 23MSCh. 4.3 - Prob. 24MSCh. 4.3 - Prob. 25MSCh. 4.3 - Power beyond the mathematics. Provide several...Ch. 4.3 - Special K. As a student at the University of...Ch. 4.3 - Special x. Find all values of x satisfying the...Ch. 4.3 - In search of x. Solve each equation for x:...Ch. 4.3 - Adding a square. Your school Healthy Eating garden...Ch. 4.3 - Golden Pythagoras (H). If you have a Golden...Ch. 4.4 - To tile or not to tile. Which of the following...Ch. 4.4 - Shifting Into symmetry. Shown below are small...Ch. 4.4 - Prob. 3MSCh. 4.4 - Prob. 4MSCh. 4.4 - Symmetric scaling (ExH). Each of the two patterns...Ch. 4.4 - Build a super. Draw a 1,2,5 right triangle in the...Ch. 4.4 - Another angle. Look at the 5-unit super-tile you...Ch. 4.4 - Super-super. Surround your 5-unit super-tile with...Ch. 4.4 - Expand forever (H). If you continue the process of...Ch. 4.4 - Prob. 10MSCh. 4.4 - Expand again. Take your 4.unit equilateral...Ch. 4.4 - One-answer supers. Here is a Pinwheel Pattern. For...Ch. 4.4 - Prob. 14MSCh. 4.4 - Many answer supers (H). Shown here are pictures of...Ch. 4.4 - Fill er up? (ExH) For each tile below, could...Ch. 4.4 - Prob. 18MSCh. 4.4 - Prob. 19MSCh. 4.4 - Prob. 20MSCh. 4.4 - Penrose tiles. Roger Penrose constructed two tiles...Ch. 4.4 - Expand forever. Why does any shape that can be...Ch. 4.4 - Super total. Recall that the Pinwheel Triangle has...Ch. 4.4 - Prob. 26MSCh. 4.4 - XY-tiles. The trapezoidal tile on the left has one...Ch. 4.4 - School spirit. Your dorm bathroom is tiled using...Ch. 4.4 - T-total (H). Suppose you start with one small...Ch. 4.5 - Its nice to be regular. What makes a polygon a...Ch. 4.5 - Keeping it Platonic. What makes a solid a regular...Ch. 4.5 - Countem up. How many faces, edges, and vertices...Ch. 4.5 - Defending duality. Explain why the cube and the...Ch. 4.5 - The eye of the beholder. Suppose you have models...Ch. 4.5 - Drawing solids. Draw each solid by completing the...Ch. 4.5 - Count. For each of the regular solids, take the...Ch. 4.5 - Soccer counts (ExH). Look at a soccer ball. Take...Ch. 4.5 - A solid slice (S). For each regular solid, imagine...Ch. 4.5 - Siding on the cube. Suppose we start with the...Ch. 4.5 - Cube slices (H). Consider slicing the cube with a...Ch. 4.5 - Dual quads (S). Suppose you have a cube with edges...Ch. 4.5 - Super dual. Suppose you take a cube with edges of...Ch. 4.5 - Self-duals. Suppose you have a tetrahedron having...Ch. 4.5 - Not quite regular (ExH). Suppose you allow...Ch. 4.5 - Truncated solids. Slice off all the vertices of...Ch. 4.5 - Stellated solids. Take each regular solid and...Ch. 4.5 - Prob. 24MSCh. 4.5 - Here we celeb rate the power of algebra as a...Ch. 4.5 - Here we celeb rate the power of algebra as a...Ch. 4.5 - Here we celeb rate the power of algebra as a...Ch. 4.5 - Here we celeb rate the power of algebra as a...Ch. 4.5 - Here we celeb rate the power of algebra as a...Ch. 4.6 - Walkind the walk. Here are three walks from corner...Ch. 4.6 - Missing angle in action. The triangles below are...Ch. 4.6 - Slippery X. A triangle is drawn on a sphere. Can...Ch. 4.6 - A triangular trio. The sphere below has three...Ch. 4.6 - Saddle sores. The triangle at right is drawn on a...Ch. 4.6 - Travel agent. In each of the following three...Ch. 4.6 - Travel agent. In each of the following three...Ch. 4.6 - Travel agent. In each of the following three...Ch. 4.6 - Latitude losers (H). In each of the following...Ch. 4.6 - Latitude losers (H). In each of the following...Ch. 4.6 - Latitude losers (H). In each of the following...Ch. 4.6 - Spider and bug. For each pair of points on the...Ch. 4.6 - Spider and bug. For each pair of points on the...Ch. 4.6 - Spider and bug. For each pair of points on the...Ch. 4.6 - Spider and bug. For each pair of points on the...Ch. 4.6 - Spider and bug. For each pair of points on the...Ch. 4.6 - Big angles (H). What is the largest value we can...Ch. 4.6 - Many angles (S). Draw three different great...Ch. 4.6 - Quads in a plane. Measure the sum of the angles of...Ch. 4.6 - Quads on the sphere. Below are quadrilaterals on...Ch. 4.6 - Parallel lines (ExH). On a plane, if you draw a...Ch. 4.6 - Cubical spheres (ExH). Take a cube. Put a point in...Ch. 4.6 - Tetrahedral spheres. Lets do a similar calculation...Ch. 4.6 - Dodecahedral spheres. This Mindscape is the same...Ch. 4.6 - Total excess. Using the observations from the...Ch. 4.6 - What is the sum of the three angles? Why? Consider...Ch. 4.6 - What is the sum of the angles of your triangle? Is...Ch. 4.6 - Removing a slice of the pie. Complete the...Ch. 4.6 - Conjuring up a conjecture. Make a conjecture about...Ch. 4.6 - Tetrahedral angles. What is the sum of the angles...Ch. 4.6 - Here we celebrate the power of algebra as a...Ch. 4.6 - Here we celebrate the power of algebra as a...Ch. 4.6 - Here we celebrate the power of algebra as a...Ch. 4.6 - Here we celebrate the power of algebra as a...Ch. 4.6 - Here we celebrate the power of algebra as a...Ch. 4.7 - At one with the univers. Below is a sketch of a...Ch. 4.7 - Are we there yet? Why does the information x=4 not...Ch. 4.7 - Plain places. Plot the following points in the...Ch. 4.7 - Big stack. If you take a huge number of sheets of...Ch. 4.7 - A bigger stack. If you take a huge number of...Ch. 4.7 - On the level in two dimensions. Pictured in the...Ch. 4.7 - On the level in two dimensions (S). Pictured in...Ch. 4.7 - On the level in four dimensions. Pictured in the...Ch. 4.7 - Tearible 2s. In the pictures below, describe how...Ch. 4.7 - Dare not to tear? For the figures in the Tearible...Ch. 4.7 - Unlinking (H). Using the fourth dimension,...Ch. 4.7 - Unknotting. Describe how you would unknot the...Ch. 4.7 - Prob. 13MSCh. 4.7 - Edgy hypercubes (H). Produce drawings of the...Ch. 4.7 - Prob. 15MSCh. 4.7 - Prob. 16MSCh. 4.7 - Doughnuts in dimensions. Suppose we have a...Ch. 4.7 - Assembly required (S). As promised in the...Ch. 4.7 - Slicing the cube. Take a 3-dimensional cube...Ch. 4.7 - Here we celebrate the power of algebra as a...Ch. 4.7 - Here we celebrate the power of algebra as a...Ch. 4.7 - Here we celebrate the power of algebra as a...Ch. 4.7 - Here we celebrate the power of algebra as a...Ch. 4.7 - Here we celebrate the power of algebra as a...
Knowledge Booster
Similar questions
- 5. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.AE.003. y y= ex² 0 Video Example x EXAMPLE 3 (a) Use the Midpoint Rule with n = 10 to approximate the integral कर L'ex² dx. (b) Give an upper bound for the error involved in this approximation. SOLUTION 8+2 1 L'ex² d (a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.) dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)] 0.1 [0.0025 +0.0225 + + e0.0625 + 0.1225 e0.3025 + e0.4225 + e0.2025 + + e0.5625 €0.7225 +0.9025] The figure illustrates this approximation. (b) Since f(x) = ex², we have f'(x) = 0 ≤ f'(x) = < 6e. ASK YOUR TEACHER and f'(x) = Also, since 0 ≤ x ≤ 1 we have x² ≤ and so Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final answer to five decimal places.) 6e(1)3 e 24( = ≈arrow_forward1. Consider the following preference ballots: Number of voters Rankings 6 5 4 2 1st choice A DCB DC 2nd choice B B D 3rd choice DCBD 4th choice CA AAA For each of the four voting systems we have studied, determine who would win the election in each case. (Remember: For plurality with runoff, all but the top two vote-getters are simultaneously eliminated at the end of round 1.)arrow_forwardPractice k Help ises A 96 Anewer The probability that you get a sum of at least 10 is Determine the number of ways that the specified event can occur when two number cubes are rolled. 1. Getting a sum of 9 or 10 3. Getting a sum less than 5 2. Getting a sum of 6 or 7 4. Getting a sum that is odd Tell whether you would use the addition principle or the multiplication principle to determine the total number of possible outcomes for the situation described. 5. Rolling three number cubes 6. Getting a sum of 10 or 12 after rolling three number cubes A set of playing cards contains four groups of cards designated by color (black, red, yellow, and green) with cards numbered from 1 to 14 in each group. Determine the number of ways that the specified event can occur when a card is drawn from the set. 7. Drawing a 13 or 14 9. Drawing a number less than 4 8. Drawing a yellow or green card 10. Drawing a black, red, or green car The spinner is divided into equal parts. Find the specified…arrow_forward
- Problem 1.We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.(d) We assume that you sell the American put to a market participant A for the pricefound in (b). Explain how you act on the market…arrow_forwardWhat is the standard scores associated to the left of z is 0.1446arrow_forward2. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.015. Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) ASK YOUR TEACHER 3 1 3 + dy, n = 6 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rule Need Help? Read It Watch Itarrow_forward
- This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one. A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture. B A B at some instant, the piston will be tangent to the circle (a) Express the x and y coordinates of point A as functions of t: x= 2 cos(3πt) and y= 2 sin(3πt) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot (3πt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +41/1 (d) Express the slope of the rod…arrow_forwardConsider the proof below: Proposition: If m is an even integer, then 5m +4 is an even integer. Proof: We see that |5m+4=10n+4 = 2(5n+2). Therefore, 5m+4 is an even integer. **Note: you may assume the proof is valid, just poorly written. Based upon the Section 1.3 screencast and the reading assignment, select all writing guidelines that are missing in the proof. Proof begins by stating assumptions ✓ Proof has an invitational tone/uses collective pronouns Proof is written in complete sentences Each step is justified ☐ Proof has a clear conclusionarrow_forwardNote: The purpose of this problem below is to use computational techniques (Excelspreadsheet, Matlab, R, Python, etc.) and code the dynamic programming ideas seen inclass. Please provide the numerical answer to the questions as well as a sample of yourwork (spreadsheet, code file, etc.).We consider an N-period binomial model with the following properties: N = 60, thecurrent stock price is S0 = 1000; on each period, the stock price increases by 0.5% whenit moves up and decreases by 0.3% when it moves down. The annual interest rate on themoney market is 5%. (Notice that this model is a CRR model, which means that thebinomial tree is recombining.)(a) Find the price at time t0 = 0 of a (European) call option with strike price K = 1040and maturity T = 1 year.(b) Find the price at time t0 = 0 of a (European) put option with strike price K = 1040and maturity T = 1 year.(c) We consider now, that you are at time t5 (i.e. after 5 periods, which represents 1month later). Assume that the stock…arrow_forward
- 4. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.024. Find the approximations Tη, Mn, and S, to the integral computer algebra system.) ASK YOUR TEACHER PRACTICE ANOTHER 4 39 √ dx for n = 6 and 12. Then compute the corresponding errors ET, EM, and Es. (Round your answers to six decimal places. You may wish to use the sum command on a n Tn Mn Sp 6 12 n ET EM Es 6 12 What observations can you make? In particular, what happens to the errors when n is doubled? As n is doubled, ET and EM are decreased by a factor of about Need Help? Read It ' and Es is decreased by a factor of aboutarrow_forward6. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.001. ASK YOUR TEACHER PRACTICE ANOTHER Let I = 4 f(x) dx, where f is the function whose graph is shown. = √ ² F(x 12 4 y f 1 2 (a) Use the graph to find L2, R2 and M2. 42 = R₂ = M₂ = 1 x 3 4arrow_forwardThe general solution X'=Ax is given. Discuss the nature of the solutions in a neighborhood of (0,0) -2-2 (²) |a) A = (23) X(A) = (₁ (fi)e* + (2 (2) eht -2-5arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell