Suppose p > 3 is a prime. Show that (p − 3)!= − P+1 (mod p). Hint: Use Wilson's theorem.

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Q: Q2: Using the Laplace transform, find the solution for the following equation y"" +y" = 6et + 6t +…

A: STEP 1 ​​STEP 2 ​​  STEP 3 ​​ STEP 4 ​​  STEP 5 ​​

Q: 1   2   3   4   5   6   7   8   9   10 Question 9   Suppose a charity…

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A: Formula for Rate of Change (ROC)The formula for calculating the average rate of change is:ROC=Change…

Q: 8. For each of the following functions, determine whether or not it is (i) injective and/or (ii)…

A: Function (a): f1: Z → Z defined by f1(n) = 2n Step 1: Check Injectivity A function f is injective…

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Q: Refer to page 34 for deriving and applying Pontryagin's Maximum Principle. Instructions: ⚫ Define…

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Q: Please help with a detailed explaintion on how to answer this question

A: Given function:f(x) = 1 / x Horizontal Stretch by a Factor of 2A horizontal stretch by a factor of k…

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Q: Can you evalutate the following summation:∑_{y=1}^{x} 2 / ((x + y - 1)(x + y + 1))

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Q: Use the Cauchy Riemann equations in polar form to show where it is holomorphic. Then use the formula…

A: Step 1: The function is:  f(z)=e−θcos(ln(r))+ie−θsin(ln(r))  z=re−iθx=∣z∣ ,  θ=arg(z) Explanation:…

Q: Refer to page 10 for properties of Banach and Hilbert spaces. Instructions: 1. Analyze the normed…

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Q: 2) Find the general solution to the following differential equation. d²x dt² - dx 6 +25x = 64e¯* dt

A: Solution:This is a second-order linear, non-homogeneous differential equation of the…

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Q: 4.3 Perform the same computation as in Prob. 4.2, but use the Maclaurin series expansion for sin x…

A: Step 1:   We will use the Maclaurin series expansion for sin⁡x  to approximate  sin(π/6).Step 1:…

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Q: 8 √x+...∞ If, y = x + √ x + √x + √x +. then y(2) =? 00

A: Step 1: Set the infinite radical as variable y. y=x+x+x+x+...∞​​​ Take the square root of both…

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A: Movie theater tickets and home movie rentals are substitute goodsAfter the reduction of the price of…

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A: Step 1:Step 2: Step 3: Step 4:

Q: Q4 4 Points 3 Let A = 5 -1 Let S : R³ → R² be the linear transformation whose standard matrix is A.…

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Q: For each real-valued nonprincipal character X mod 16, verify that L(1,x) 0.

A: To verify that L(1, χ) ≠ 0 for each real-valued non principal Dirichlet character χ modulo 16, we…

Q: please solve handwritten without use of AI

A: Step 1:Step 2: Step 3: Step 4:

Q: 3. A market consists of two risky assets with rates of return R₁ and R2 and no risk-free asset. From…

A: Step-by-Step Solution Given Data We have two risky assets with the following parameters: Expected…

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A: Let's go through the solution step by step in detail.if 2 is multiple than -

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A: The given augmented matrix represents a system of linear…

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A: The number of paths is the total number of ways we can travel from A to H.A to B: 2 edges.A to C: 3…

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A: Question 3Explanation:In the given graph of f'(x), we can observe the following:From x = 0 to x = 2,…

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Q: When P is True and Q is False, what is the truth value of (P→ ~Q)? a. True ○ b. False c. unknown

A: We are asked to evaluate the truth value of the expression, P→¬Q, given that:P is True.Q is…

Q: No chatgpt pls will upvote

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

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A: If you have any help please let me know in comment box thankyou.

Q: Given the (3-2-1) Euler angle set (10,20,30) degrees, find the equivalent (3-1-3) Euler angles. All…

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A: Step 1: Calculate Option 1 (Simple Interest)The formula for simple interest is:Simple…

Q: 7. Rank and Nullity • Prove the Rank-Nullity Theorem: dim(ker(T)) + dim(im(T)) = dim(V) for a linear…

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Q: Question 3 (a) Find the principal part of the PDE AU + UÃ + U₁ + x + y = 0 and determine whether…

A: Step 1:Brief Explanation(a) Principal Part and ClassificationPrincipal part: The highest-order…

Q: lim 1 x→0x3 L 0 X ln(1+t) dt t4 +4

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Q: 5. Find the greatest common divisor (GCD) of 24 and 36. 6. Is 121 a prime number? If not, find its…

A: 5). Finding the GCD of 24 and 36: Step 1: List the factors of each number. Factors of 24: 1, 2, 3,…

Q: No chatgpt pls will upvote Already got wrong chatgpt answer Plz

A: Step 1:Step 2:Step 3:Step 4:

Q: Question 3 (a) Find the principal part of the PDE AU + Ux +U₁ + x + y = 0 and determine whether it's…

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Q: Exilet x = {a,b.c}dex.x―R> d(a,b) = d(b, c)=1' d(a, c) = 2 d(xx)=0VXEX is (x.d) m.s or not? 3.4 let…

A: Detailed explanation:

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A: (a) Convert All Amounts to Monthly AmountsFor amounts not already monthly, we convert as…

Q: Assignment Brief: 1. Use the trapezium rule with five ordinates (four strips) to find an…

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Q: Let A be a 4 x 4 matrix with the following characteristic polynomial: a) Find the eigenvalues of A.…

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A: (a)(b)

Q: Define sinc(x) = sin(x)/x, except with the singularity removed.  Differentiate sinc(x) once and…

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Q: 9. [10 marks] Consider the following graph G. (a) Find the Hamilton closure of G. Explain why your…

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Q: 7. Define the sequence {b} by bo = 0 Ել ։ = 2 8. bn=4bn-1-4bn-2 for n ≥ 2 (a) Give the first five…

A: Step 1: