I have first part of question good. Need to prove unique modulo and do not know where to start.
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I have first part of question good. Need to prove unique modulo and do not know where to start. Prove that the congruences x-a mod n and x b mod m admit a simultaneous solution if and only if (n, m)...
We know that we can reduce the base of an exponent modulo m: a(a mod m)k...
We know that we can reduce the base of an exponent modulo m: a(a mod m)k (mod m). But the same is not true of the exponent itself! That is, we cannot write aa mod m (mod m). This is easily seen to be false in general. Consider, for instance, that 210 mod 3 1 but 210 mod 3 mod 3 21 mod 3-2. The correct law for the exponent is more subtle. We will prove it in steps (a)...
6.32 Theorem. If k and n are natural numbers with (k, d(n)) =I, then there exist positive integers u and v satisfving k...
6.32 Theorem. If k and n are natural numbers with (k, d(n)) =I, then there exist positive integers u and v satisfving ku=(n)u The previous theorem not only asserts that an appropriate exponent is always availahle, but it also tells us how to find it. The numbers u and are solutions lo a lincar Diophantine cquation just like those we studied in Chapter 6.33 Exercisc. Use your observations so far to find solutions to the follow ing congruences. Be sure...
Problem 5 (a) Let A be an n × m matrix, and suppose that there exists a m × n matrix B such that BA = 1- (i) Let b є Rn be such that the system of equations Ax b has at least one solution. Prove that...
Problem 5 (a) Let A be an n × m matrix, and suppose that there exists a m × n matrix B such that BA = 1- (i) Let b є Rn be such that the system of equations Ax b has at least one solution. Prove that this solution must be unique. (ii) Must it be the case that the system of equations Ax = b has a solution for every b? Prove or provide a counterexample. (b) Let...
4. (a) For n eZ, define multiplication mod n by ao b-a b (where indicates regular...
4. (a) For n eZ, define multiplication mod n by ao b-a b (where indicates regular real number multiplication), prove that On is a binary operation on Zn. That is, (Hint your proof will be very similar to the proof for homework 4 problem 7ab) (b) Let n E Z. Is the binary algebraic structure 〈L,On) always a group? Explain. (c) Prove There exists be Zn such that a n I if and only if (a, n)1. (d) It is...
I just need help with part b. I know how to do part a, but I...
I just need help with part b. I know how to do part a, but I
don't know how to go about including the competitive equilibrium
for part b
1. Suppose a monopolist producing standard paper has a monthly cost function where C(q) = ex is the quantity produced by each firm. Monthly demand for standard paper is p=-oxi. (a) What is the marginal revenue function of the firm? What is the marginal cost function of the firm? The profit...
Can I know how to do part(c)? I know how to do (a)(b). By (a) and...
Can I know how to do part(c)? I know how to do
(a)(b).
By (a) and (b), I get this 4 results.
1. ▾.F = 2xz5-2xz+3xz2
2. ▾xF = (2xy) i + (5x2z4-z3) j
-(2yz) k
3. ▾.(▾xF) = 0
4. ▾x(▾f) = 0
Next, i need to calculate part (c).
I want the solution of part(c), so don't give me the result of
part(a) and (b) again,
thanks!
1. (25 marks) (a) Evaluate . F and V. (V x...
I need to know how to do part c only. Constants A 2.00-kg, frictionless block is...
I need to know how to do part
c only.
Constants A 2.00-kg, frictionless block is attached to an ideal spring with force constant 300 N/m. Att 0 the block has velocity -4.00 m/s and displacement +0.200 m.
I need help with number 3 on my number theory hw. Exercise 1. Figure out how...
I need help with number 3 on my number theory
hw.
Exercise 1. Figure out how many solutions x2 = x (mod n) has for n = 5,6,7, and then compute how many solutions there are modulo 210. Exercise 2. (a) Find all solutions to x2 +8 = 0 (mod 11). (b) Using your answer to part (a) and Hensel's Lemma, find all solutions to x2 +8 = 0 (mod 121). Exercise 3. Solve f(x) = x3 – x2 +...
do not know where to start on part c and d 11. Propanoic acid, HC3H,O2, ionizes...
do
not know where to start on part c and d
11. Propanoic acid, HC3H,O2, ionizes in water according to the equation below K-1.34 X 10 + H3O HCH,O HO CsHsO2( a Write the equilibrium constant expression for the reaction. CHCgHO2 b. Calculate the pH of a 0.265M solution of propanoic acid. 2 Cafleo HO HC,H02H,0 I 0,265M 2 1.34 x (0 L0,265 OM OM dre 2.05x10 tx X 4 0,265-x Aog [.8x 10-M 34x 10-5 X 0,205 veglig 0.00188M-X=[H,0...
Please help me with understandable solutions for question 6(a), 7, 8 and 10. ( Use Chinese...
Please help me with understandable solutions for question 6(a), 7,
8 and 10. ( Use Chinese remainder theorem where applicable).
78 CHAPTER 5. THE CHINESE REMAINDER THEOREM 6. (a) Let m mi,m2 Then r a (mod mi), ag (mod m2) can be solved if and only if (m, m2) | a1-a2. The solution, when it exists, is unique modulo m. (b) Using part (a) prove the Chinese remainder theorem by induction. 7. There is a number. It has no remainder...
We know that we can reduce the base of an exponent modulo m: a(a mod m)k (mod m). But the same is not true of the exponent itself! That is, we cannot write aa mod m (mod m). This is easily seen to be false in general. Consider, for instance, that 210 mod 3 1 but 210 mod 3 mod 3 21 mod 3-2. The correct law for the exponent is more subtle. We will prove it in steps (a)...
6.32 Theorem. If k and n are natural numbers with (k, d(n)) =I, then there exist positive integers u and v satisfving ku=(n)u The previous theorem not only asserts that an appropriate exponent is always availahle, but it also tells us how to find it. The numbers u and are solutions lo a lincar Diophantine cquation just like those we studied in Chapter 6.33 Exercisc. Use your observations so far to find solutions to the follow ing congruences. Be sure...
Problem 5 (a) Let A be an n × m matrix, and suppose that there exists a m × n matrix B such that BA = 1- (i) Let b є Rn be such that the system of equations Ax b has at least one solution. Prove that this solution must be unique. (ii) Must it be the case that the system of equations Ax = b has a solution for every b? Prove or provide a counterexample. (b) Let...
4. (a) For n eZ, define multiplication mod n by ao b-a b (where indicates regular real number multiplication), prove that On is a binary operation on Zn. That is, (Hint your proof will be very similar to the proof for homework 4 problem 7ab) (b) Let n E Z. Is the binary algebraic structure 〈L,On) always a group? Explain. (c) Prove There exists be Zn such that a n I if and only if (a, n)1. (d) It is...
I just need help with part b. I know how to do part a, but I
don't know how to go about including the competitive equilibrium
for part b
1. Suppose a monopolist producing standard paper has a monthly cost function where C(q) = ex is the quantity produced by each firm. Monthly demand for standard paper is p=-oxi. (a) What is the marginal revenue function of the firm? What is the marginal cost function of the firm? The profit...
Can I know how to do part(c)? I know how to do
(a)(b).
By (a) and (b), I get this 4 results.
1. ▾.F = 2xz5-2xz+3xz2
2. ▾xF = (2xy) i + (5x2z4-z3) j
-(2yz) k
3. ▾.(▾xF) = 0
4. ▾x(▾f) = 0
Next, i need to calculate part (c).
I want the solution of part(c), so don't give me the result of
part(a) and (b) again,
thanks!
1. (25 marks) (a) Evaluate . F and V. (V x...
I need to know how to do part
c only.
Constants A 2.00-kg, frictionless block is attached to an ideal spring with force constant 300 N/m. Att 0 the block has velocity -4.00 m/s and displacement +0.200 m.
I need help with number 3 on my number theory
hw.
Exercise 1. Figure out how many solutions x2 = x (mod n) has for n = 5,6,7, and then compute how many solutions there are modulo 210. Exercise 2. (a) Find all solutions to x2 +8 = 0 (mod 11). (b) Using your answer to part (a) and Hensel's Lemma, find all solutions to x2 +8 = 0 (mod 121). Exercise 3. Solve f(x) = x3 – x2 +...
do
not know where to start on part c and d
11. Propanoic acid, HC3H,O2, ionizes in water according to the equation below K-1.34 X 10 + H3O HCH,O HO CsHsO2( a Write the equilibrium constant expression for the reaction. CHCgHO2 b. Calculate the pH of a 0.265M solution of propanoic acid. 2 Cafleo HO HC,H02H,0 I 0,265M 2 1.34 x (0 L0,265 OM OM dre 2.05x10 tx X 4 0,265-x Aog [.8x 10-M 34x 10-5 X 0,205 veglig 0.00188M-X=[H,0...
Please help me with understandable solutions for question 6(a), 7,
8 and 10. ( Use Chinese remainder theorem where applicable).
78 CHAPTER 5. THE CHINESE REMAINDER THEOREM 6. (a) Let m mi,m2 Then r a (mod mi), ag (mod m2) can be solved if and only if (m, m2) | a1-a2. The solution, when it exists, is unique modulo m. (b) Using part (a) prove the Chinese remainder theorem by induction. 7. There is a number. It has no remainder...
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