Question: If x; y; z R and x < z, show that x < y < z if and only if |x - y| +

If x; y; z ∈ R and x < z, show that x < y < z if and only if |x - y| + |y - z| = |x - z|. Interpret this geometrically.

Step by Step Solution

★★★★★

3.47 Rating (163 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

If x y z then x y y z y x z y z x z x To establi... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

829-C-I (939).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Q:

A wood beam AB on simple supports with span length equal to 10 ft is subjected to a uniform load of intensity 125 lb/ft acting along the entire length of the beam, a concentrated load of magnitude...

Q:

For each of the following relations, determine whether the relation is reflexive, symmetric, antisymmetric, or transitive. (a) R Z+ Z+ where a R b if a|b (read "a divides b," as defined in Section...

Q:

If r = (x, y, z), a = (a 1 , a 2 , a 3 ), and b = (b 1 , b 2 , b 3 ), show that the vector equation (r - a) (r - b) = 0 represents a sphere, and find its center and radius.

Q:

Assume that all the given functions are differentiable. If z = f (x, y), where x = r cos and y = r sin , (a) find z/r and z/ and (b) show that -'-- r? ar

Q:

Part 1 - Data Encryption Data Encryption is the process of transforming data, using a cipher, to make it unreadable to anyone except those possessing special knowledge. In this problem you will...

Q:

2. (8 points) Write an assembly program to compute the following expressions Z = X + 6 Z r+ y - 9 where x, y, r and z are 16-bit integer memory variables. - x = 7, y= 20, r = 4 - z is a list. (you...

Q:

Flow control mechanisms in networks can be loosely categorised as open loop, and closed loop. (i) Describe the closed loop feedback control scheme employed by the Transmission Control Protocol (TCP)...

Q:

Define the contextual-equivalence relation ` M =ctx M0 : for pairs of PCF terms M, M0 , PCF types , and PCF type environments . [3 marks] (ii) For PCF terms M and N with respective typings ` M : and...

Q:

Let r = (x, y, z) and e r =r/ r. Show that if a function (x, y, z) = F(r) depends only on the distance from the origin r = r= x 2 + y 2 + z 2 , then Vf = F'(r)er

Q:

Let V be the vector space R. (a) Let W = {(x, y, z) = R : z = x + y}. Is W a subspace of V? Give reasons. == (b) Let U = {(x, y, z) = R z = x} Is U a subspace of V? Give reasons.

Q:

Please show all work in the space provided to receive partial credit. Please box in your answers. Use the following sets to answer the questions 1-3 that follow: U = {x x is a letter of the alphabet]...

Q:

Big Country Ski Shop is a retail store that sells ski equipment and clothing. Big Country Ski Shop commenced business on September 1, 2019. The firm purchases merchandise on open account. The firms...

Q:

Capacitors C1 = 4.0 F and C2 = 2.0 F are charged as a series combination across a 100-V battery. The two capacitors are disconnected from the battery and from each other. They are then connected...

Q:

Which of the following is an example of a liability? A) Equipment B) Accounts Receivable C) Accounts Payable D) Inventory

Q:

For the Excel file Credit Approval Decisions, find 95% confidence and prediction intervals for the credit scores and revolving balance of homeowners and nonhomeowners. How do they compare?

Q:

(a) When may a corporation sell, lease, exchange, mortgage, or pledge all or substantially all of its assets in the usual and regular course of its business? (b) When may a corporation sell, lease,...

Q:

1. Explain how the Sports Exports Company could utilize the spot market to facilitate the exchange of currencies. Be specific. 2. Explain how the Sports Exports Company is exposed to exchange rate...

Q:

Of the $10,000 invested in a two-stock portfolio, 30 percent is invested in Stock A and 70 percent is invested in Stock B. If Stock A has a beta equal to 2.0 and the beta of the portfolio is 0.95,...

Q:

(Issuance and Retirement of Bonds) Venezuela Co. is building a new hockey arena at a cost of $2,500,000. It received a down payment of $500,000 from local businesses to support the project, and now...

Q:

(Changes in Government Purchases) Assume that government purchases decrease by $10 billion, with other factors held constant, including the price level. Calculate the change in the level of real GDP...

Q:

The figure shows a curve C with the property that, for every point P on the middle curve y = 2x2, the areas A and B re equal. Find an equation for C. y 2x2

Q:

(a) What is the volume of a cylindrical shell? (b) Explain how to use cylindrical shells to find the volume of a solid of revolution. (c) Why might you want to use the shell method instead of slicing?

Q:

(a) What is the average value of a function f on an interval [a, b]? (b) What does the Mean Value Theorem for Integrals say? What is its geometric interpretation?

Q:

Pitt Enterprises manufactures jeans. All materials are introduced at the beginning of the manufacturing process in the Cutting department. Conversion costs are incurred uniformly throughout the...

Q:

Principles of Risk and Management Insurance (12 ed) Ch 21 Case Application James and Megan Webb recently purchased a home for $300,000. The home is insured under an HO-3 policy for $250,000 with no...

Q:

Andretti Company has a single product called a Dak. The company normally produces and sells 84,000 Daks each year at a selling price of $60 per unit. The company's unit costs at this level of...