Let S be the set of integer solutions to the equation ri + r2 +13+x4 = 30, where ri >0 for i = 1,2, 3, 4. That is, S= {(r1, 12, 13, 14) | r; € Z and ri > 0 and ri + 12 + 13 + 14 = 30}. (a) Find |S]. For i = 1,2,3, 4, define A, = {(r1, r2, 13, 14) ES|r; > 10}. (b) Find JA| for each i. (c) For each 1

Q: Q1) If A- ,B-3 13| Find (–1 x A) + (B+ C)

A: Given that,       A=411-2-193,  B=-5-134013,  C=75-6-19-1

Q: Let A 1 value of k. [23] A and B = 1 -7 217 k If AB = BA, find the

A:

Q: Suppose x is a real number. Prove that if x 2, then there is a real number y such that x =…

A:

Q: (4) Prove in two different ways that if a is a positive r number, then (a + 1)" > a" + na"-1:

A:

Q: Recall the property that (a, b) = 1 if and only if ax + by = 1 for some integer x, y. Use this…

A:

Q: Let a and b be positive integers. If ax + by = c has an integer solution (x, y), it is necessarily…

A: Consider the given equation. Find the characteristic for c if a, b are positive integers and ( x, y…

Q: For which real numbers x do the following equations hold: (a) Vx + V2x – 1+ Vx – V2x – 1 = V 2а — 1…

A:

Q: Find the set of real values of x for which a) > 3 by/2x- 3/ 0 13 Solve the inequality:x(x² – 6) >…

A: It is given that

Q: 8. Let a, b and c be any positive real numbers. Prove that b² + c² a²+b² 2c a² + c² + 2b 2a > a+b+c.

A:

Q: Prove that 1+6x-x is always a positive real number if x =3+Ai for some real 33 number 4

A: The given number is  1 + 6x - x2

Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: Find the number of nonnegative integer solutions to x₁ + x₂ + x3 + x4 + x5 ≤ 23. Find the number of…

A: We have to find the number of non negative integer solution of Note: According to the guidelines we…

Q: Let S = {-5,-1,0,2/3,5/6,1,sqrt(6),4,5} Determine which elements of S satisfy the inequality.…

A:

Q: 8. A (5+, 10-) where A-Z 9. Ax [5+, 10-] where A = Z' 10. Ax=(1, 10) where A = (0,1)

A: These are the problems from the Set Theory.

Q: Find a pair of values (x, y) that serve as a counter-example for the statement that [ry] : |x||y for…

A: The ceiling function gives smallest integer that is greater than the number, that is, x is the…

Q: ind the interval in the real number line which equals 1 U [4+, 20- n n=1 n

A: Answer given below.

Q: 1. (a) Prove that if alb and alc. then alb² + 10c + a.

A:

Q: The algebraic translation of "x is at most 7" is

A: Given : The algebraic translation of " x is at most 7" is ______________ .

Q: Ex. Show that V1 = 3i + 7j & V2 =i++1)j a %3D %3D are equal ?

A: Simple vector problem...

Q: a. 2 |x – 4|| х-1 b. x? + 2х — 12 1 х+1

A: a.  (1, 2] and [3, (5+√17)/2]         b.  (-1-√13 , -1+√13)

Q: Answer the question and gets thumbup plzzzzzz

A: here we use fermat little theorem

Q: 16. Find the set of real values of x for which:/3 - 2x/S/x + 4/. N.Find the set of values of x for…

A:

Q: Show that if u is an odd integer ,then the equation x2 +x−u=0 has no solution that is an integer.

A: The objective is to prove that x2+x-u=0 has no solution that is an integer. Suppose that there…

Q: The houses of a row are numbered consecutively from 1 to 49.show that there is a value of x such…

A:

Q: Use the equation y = x² - 17x + 72 to answer the following question. For what values of x is y ≥ 0?

A:

Q: 4. Ax (1-22, 1+22) where A - Z 5. Ax(0, 32, 62) where A - Z 6. A, [5, 10- +] where A = Z' 7. Ax (5+,…

A:

Q: Prove that A-B=An(-B) = (-B) – (-A) = −[(-A) U B]. Also, give three expressions for An B and AU B,…

A: Difference of sets: Given two sets A and B, the difference A−B is defined as the set of all elements…

Q: Prove by contradiction method : if x>0  then 2 ≤ x + 1/2

A:

Q: 5 Find the least common denominator of X 11 and 4 8x+5' X 3

A:

Q: If z≤2, show that |Im(5 + 2z - 3z³)| ≤ 33.

A: The given problem is to show the given identity for the given condition |z|≤2. Given identity,…

Q: Find I(3/2), I(-1/2), and I(-3/2) in terms of n

A: Γ 32=∫0∞t32-1e-tdt=∫0∞t12e-t=0.282π

Q: 9. 12 (7x + 5) TW

A:

Q: If |z| ≤ 2, show that |Im(5 + 2z - 3z³)| ≤ 33.

A: We know, for a complex number z      i) |Im(z)| ≤ |z|      ii) |z̄| = |z| Also, for any two complex…

Q: Let x, y, and z be real numbers. Prove the following a. -(-x) = x b. (-x) * (y) = -(xy) and (-x) *…

A: I have provided detailed proof for each question in the Explanation section.Explanation:Let's go…