What is the congruence class [4] when m is b) 37 c) C) 6? 67

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Q: Prove the following. 1. The sum of four consecutive integers is even.

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A: Given that in an examination, the maximum marks for three papers are 50 and fourth paper has maximum…

Q: - what number a discountinuous what number and why, why 9 differentiable and g

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Q: 5. Suppose that f: R R is a continuously differentiable function (of class C¹) and that there is a…

A: The solution will depend on the following three theorems which we recall. 1. Inverse Function…

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A: Provided that  A is set of different triangles in the plane and B is set of all positive real…

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Q: 2. Suppose ƒ'(x) = (x − 1)¹⁰ (x + 2)⁹999 (x + 3)(x + 5)³(x − 2)¹2000. Find all values of x for which…

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Q: 1. For each of the following statements, determine if the conclusion ALWAYS follows from the…

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Q: 2y" + 3y' - 2y = 3xez* - 2sinлx (Use Method of Undetermined Coefficients (MUC))

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Q: f d a h C 6.0 g e b

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Q: 10) Use the graph to the right to answer the following questions. a) For what values of x is f(x)…

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Q: 3. Determine if the following limit exists and give its value if it does. log z lim 2-1 2-1

A: We use the definition of the derivative to solve this problem. That is we adjust the limit in such a…

Q: Set up a triple integral in cylindrical coordinates for the volume of the solid region E, where E is…

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Q: Find the accumulated amount A, if the principal P is invested at an interest rate of r per year for…

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Q: IF AN ITEM IS VALID (V), THEN SHOW THAT IT IS VIA PROOF OF VALIDITY (S); BUT IF IT IS NOT VALID.…

A: The first statement (premise) is P  ≡ "If I'm tired [T] or bored [B] then I sleep [S]"      ≡ T v B…

Q: 12. Using the Sheffer stroke, or NAND (not-and) operator, logically equivalent: a. pla~(pa) b. p/p…

A: We prove these statements using truth table.

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A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

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A: We will find the area of the shaded region using the z score table.  We know P(-2.41<z<2.49) =…

Q: = eat. Use 4. Consider the equation x" - 2ax' + a²x = 0, which has solution x = reduction of order…

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Q: Of the 46 plays attributed to a playwright, 11 are comedies, 15 are tragedies, and 20 are histories.…

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Q: 12. Prove using both the pick a point method and the algebraic method For each set, A, B, and C, (A^…

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Q: List the critical numbers of the following function in increasing order. Enter N in any blank that…

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Q: Introduce slack variables as necessary, then write the initial simplex tableau for the linear…

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Q: Solve the one-dimensional Laplace equation for the equilibrium temperature distribution in a finite…

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Q: You are given the first five terms of the sequence, namely t₁, t2, t3, ta, ts. (a) 99,94, 89, 84,…

A: The nth term of arithmetic sequence is tn=a+(n-1)d. The nth term of geometric sequence is tn=arn-1…

Q: In Exercises 11-14, give a formula for the cardinality rule or rules needed to answer the question,…

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Q: b) Test the convergence of the series: 3 * 4 2 * 3+ 22√2 where * denotes usual multiplication. + 4 *…

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Q: 6. Find the negation of the following statements: a. p:0≥x>5 b. q:4+5<10 c. r: Manila is the capital…

A: Q6 a-e asked and answered.

Q: EXERCISES 1. Find the general solution of x" + tx' + x = 0 given that x = e-t²/2 is one solution. 2.…

A: Given Data: To show that x1t=t is a solution of the equation x''-tx'+x=0 To find: The second…

Q: 1. Given U={x|xEZ,5≤x≤20) and its three subsets: A={alaEU,a is even), B={b]bEU, b=10), C = {c | CEU,…

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Q: Consider the non-linear autonomous system of differential equations dx dt dy dt =y-1 y x² + 2x - 1…

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Q: Determine whether each of these functions from R to R is a bijection. f(x) = x3

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Q: Examine each of the following relations given below and stat in each case, giving reasons whether it…

A: (i) Since 4, 5, 6 are the elements of domain of R having their unique images, this relation R is a…

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Q: Question 6 For the function h: [0, 2] → R defined by 2x + 1 x = [0, 1] 3-x x = (1, 2] prove using…

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Q: Set up a triple integral in cylindrical coordinates for the volume of the solid region E, where E is…

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Q: Show all necessary solutions and justify answers 3. Prove: For any real numbers x and y, with x 0,…

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Q: 4. Solve the IVP of y"+2y+y=0, y(0) = 4, y(0)=-6.

A: Since you have posted a multiple question according to guildlines I will solve first(Q4) question…

Q: Find and classify the critical points of z = (x² − 2x) (y² – 5y). Local maximums: Local minimums:…

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Q: .00 #fishow that e-x² dx = √n by considering e-(x²+y²) dxdy and a conversion to polar coordinates.

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Q: Calculating First-Order Partial Derivatives In Exercises 1-22, find af/ax and af/ay. 17. f(x, y) =…

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Q: 322. 2x49x³ +5x² - 3x6 is divided by x-4

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Q: 2. Let T: R³ R³3 be the linear transformation defined by T((x, y, z)) = (x+z, -y-z, 2x+y+3z). a.…

A: Linear transformation and ker of T

Q: Find two mistakes in the following 'proof' and give a counterexample that shows wh the claim can't…

A: We have to find errors in the given proof. Also, We have to find a counter example for the…

Q: Compute A² and hence determine A-¹. Demonstrate this cryptography scheme using the secret key A by:…

A: The secret key given is as follows: A=320-4-3000-1 (a) We have to compute A2 and hence A-1. We will…