Find the value of arcsin ? A. 3 B. Í C. D. ОС o A B
Problem 2. Find (with proof) all positive integers n that have an odd number of positive divisors (for example 6 has 4 positive divisors 1,2,3,6).
Discrete Structures class. An ordered triple of positive integers (a,b,c) is called a Pythagorean Triple if a^2 + b^2 = c^2. Prove that if m & n are pos int.... 2) (10 pts) An ordered triple of positive integers (a, b, c) is called a Pythagorean Triple if a² + b2 = c2. Prove that if m and n are positive integers with m > n, then (m? – nº, 2mn, m² + n°) is a Pythagorean triple. Use this...
2. Prove that if a and b are positive integers such that a is a factor of b, then any finite (terminating) mantissa of base a can be converted to a finite (terminating) mantissa of base b. Note: Express the number in summation form
1 For each of the following pairs of numbers a and b, calculate and find integers r and s such ged (a; b) by Eucledian algorithm that gcd(a; b) = ra + sb. ia= 203, b-91 ii a = 21, b=8 2 Prove that for n 2 1,2+2+2+2* +...+2 -2n+1 -2 3 Prove that Vn 2 1,8" -3 is divisible by 5. 4 Prove that + n(n+1) = nnīYn E N where N is the set of all positive integers....
The product of two consecutive integers is 42. Find all such pairs of integers. The positive set of integers: x = and x+1 = The negative set of integers: x = and x+1 =
Find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have the following properties: (a) are divisible by 5 and by 7. (b) have distinct digits. (c) are not divisible by either 5 or 7.
consider two vectors A= -10i+20j, and B has a length of 15 and angle of +45 with respect to the positive x axis. What third vector C must be added to these two such that A+B+C=0?
(on this page, A, B, C, D are all positive integers and A/B <C/D.) We saw in the previous assignment that CA CB - AD 1 DB=BD ? BD (The numerator must be an integer, and since the two fractions are unequal, it can't be 0.) In other words, "the closest two unequal rational numbers and can be is BD" (9.1) A sort of average of two fractions: . Show that <A+O- We gave an intuitive explanation of this in...
Recall we say that a Pythagorean triple is a triplet of positive integers a, b and c such that a^2 + b^2 = c^2. Examples are (3,4,5) and (5,12,13). Explain why for any Pythagorean triplet one must have that 12 divides abc. (Hint: It may be easiest to do this by showing that 3 divides abc and showing separately that 4 divides abc).