2. is a positive real number with .
[ Since ]
[ Since ]
So ,
Hence ,
Answer : .
Question 2 (7 points) If b is a positive real number with b + 1, then...
We write R+ for the set of positive real numbers. For any positive real number e, we write (-6, 6) = {x a real number : -e < x <e}. Prove that the intersection of all such intervals is the set containing zero, n (-e, e) = {0} EER+
We write R+ for the set of positive real numbers. For any positive real number e, we write (-6, 6) = {x a real number : -e < x <e}. Prove that the intersection of all such intervals is the set containing zero, n (-e, e) = {0} EER+
Question 13 (0.5 points) For all positive integers a and b, if al0 = 1 (mod b) then a = 1 (mod b). True False Question 14 (0.5 points) For all positive integers an, az, mi and m2, if mı #m2 then the system of linear congru- ences x =ai (mod mi) x = a2 (mod m2) admits at most one solution modulo mim2. True O False Question 15 (0.5 points) For all positive integers a and b, if a|b2...
can you please help me with number 2 and 3? thanks Problem 2. Consider a version of question 9 from the first WebWork problem set and an attempt at solving it. Find and explain the 3 mistakes that were made. Use the line numbers to identify where they occurred. Question 9: If a (base 10) double-log plot displays a line through the points (-3, -2) and (5,5), find the relation between x and y. Solution attempt: First, a correct double-log...
QUESTION 9 log8 (16)-1098 (2) = O 14 QUESTION 10 True or False: The domain of the log function is all real numbers. O True ︶ False QUESTION 11 What is the domain of the function f(x) -In (x-3) all real numbers
Need help, will rate, thanks. In class, we noticed something interesting: (-1) 2 4 This motivates a natural question: whether or not there exist other pairs of distinct real numbers x and y such that To avoid square-roots of negatives (complex numbers), we consider only pos- itive values of a and y. We use a graph to get us started: 0.5 0,5 Figure 1: The Solution Set for y. (Graphic created with Desmos) The line y = x isn't of...
Absolute value is always... 1. Positive 2. Non-negative Every fraction is a rational number. True or False? The sum of 2/3 and 5/7 is 7/10. True or False? The quotient of two fractions cannot be a whole number True or False? The set of whole numbers is a subset of the set of rational numbers. True or False? Which of these fractions is between 7/13 and 14/19 ? 1. a. 6/17 2. b. 9/16 3. c. 1/2 4. d. None...
9. (5 points) Please translate this statement into English, where the domain for each variable consists of all real numbers. VrVyz(x = y + 2) 10. (5 points) Please determine the truth value of the staement Bruz Sy) if the domain for the variables consists of the nonzero real numbers. 11. (5 points) Please determine what rules of inference are used in this argument: "No man is an island. Manhattan is an island. Therefore, Manhattan is not a man." 12....
QUESTIONS #1-11 SHOULD BE COMPLETED WITHOUT THE USE OF ANY CALCULATOR!!! 1. Find the solution to the equation in (r? + 3x ) – In 10=0. a) x=5 or x = -2 b) x= -5 or x = 2 c) x = 5 d) x = 2 2. Find the solution to the equation log, 8 c) d) r=2 a) x=512 b) x=24 8 3. Solve for logs d) 0 c) -3 b) 3 a) 6 d) all rational numbers...
6. For a positive real number z, the difference 1.-z- is called the fractional part of r. Given arbitrary positive real numbers a and b, state a condition in terms of the fractional parts of and that is necessary and sufficient for la + bl = lal + Ibl Prove that this equation is true if and only if your condition holds. 7. Evaluate 10002+4 23k+5 k- 2 algebraically and simplify as much as possible. You ust show all steps....