Question: If a; b R and b 0, show that: (a) |a| = a2; (b) |a/b| = |a|/|b|.

If a; b ∈ R and b ≠ 0, show that:
(a) |a| = √a2;
(b) |a/b| = |a|/|b|.

Step by Step Solution

★★★★★

3.39 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a If a 0 then a a a 2 if a 0 then a ... 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 (932).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Q:

If a, b R and b - a > 1, then there is at least one k Z such that a

Q:

(a) Let f: AB, where |A| = 25, B = {x, y, z}, and | f-l(x) | = 10, | f-l(y) | = 10, |f-1(z)| = 5. If we define the relation R on A by a R b if a, b A and f(a) = f(b), how many ordered pairs are...

Q:

If a particle is dropped at time t = 0, physical theory indicates that the relationship between the distance traveled r and the time elapsed t is r = gtk for some positive constants g and k. A...

Q:

Let (a+ b i ) C where a, b R and b 0. Show that C = R(a + bi).

Q:

FOLLOW THE EXERCISE 2. Let a, b E R and let fab: R R be the function defined as fab(x) = ax + b for all x E R. Use this for the problems below. a) Prove that G = {fab | a, b = R, and a # 0} is a...

Q:

/mod_resource/content/1/FT-PT_CMCA_Assignment_Jan%2021_V1.pdf Question 3 (a) The wavelength 1 and frequency f of a sound wave are related by Af=v, where v is the speed of the wave. Musicians refer...

Q:

do it fassst plz and down the character table 04. Construct 3x3 matrices for three vectors representing sayma bonding only. What are possible hybrid orbitals in central metal ion (AP) in AICI? (15...

Q:

(a) A+B Write the augmented matrix for the system of linear equation possible, find AB, BA, and A2. (If not possib x - y + 82 = 6x - 5y + z= -1 A - [ 2 14]. B - [4 ] 8x + y = 0 (a) AB 1 (b) A - B AB...

Q:

Goal is to fill in the blank. A traverse surveying was performed. C ADMIN CARPARK T3 B SCIENCES Instrument Target Face left (L) or right (R) Circle Plate Reading Angle Name Corrected Angle Degrees ()...

Q:

Note: i = and j = 1. Convert the point whose polar coordinates are (V3, ?) to to rectangular coordinates. (A) 3 V3 2 ' ( B ) (21 2) (0 ) ( 3 , V3 ) ( D ) ( V3 , " ) ( E ) (V3 3 2. Which of the...

Q:

A linear time-invariant system has impulse response h[n] = u[n]. Determine the response of this system to the input x[n] shown in figure and described as 0, n

Q:

A subway train travels between two stations with the acceleration graph shown. Determine the time interval, A? such that the train brakes to a stop with a deceleration of 2 m/s, and finds the...

Q:

4 a Calculate the capacity utilization rate for Meiji Milk Company that can produce 200000 pints of milk in its factory each day but has an output level of 180000 pints per day. [2] b Calculate BF...

Q:

A physical version of the product concept that is developed during the new product development process is called a ________. a. mock-up b. model c. prototype d. precedent

Q:

In Example 1 in Section 3.8 we modeled the world population in the second half of the 20th century by the equation P(t) = 2560e0.017185t. Use this equation to estimate the average world population...

Q:

Prove the Mean Value Theorem for Integrals by applying the Mean Value Theorem for derivatives to the function F(x) = f(t) dt.

Q:

(a) Find the average value of f on the given interval. (b) Find such that fave = f(c). (c) Sketch the graph of f and a rectangle whose area is the same as the area under the graph of f. (1) f(x) = (x...

Q:

Sunland Company makes and sells umbrellas. The company is in the process of preparing its Selling and Administrative Expense Budget for the last half of the year. The following budget data are...

Q:

zivo 3G JAWWAL II. Aitc.birzeit.edu Anabtawi Company uses the periodic inventory method and had the following inventory information available: ( 8 points) Date Explanation Number Unit Total of Units...

Q:

Cooper Company has a direct materials standard of 2 gallons of input at a cost of $10.50 per gallon. During July, Cooper Company purchased and used 6.780 qalions, paying $46.600 The direct materials...