Using Fermat's little theorem, find the solutions of the following linear congruences. a) 7x ≡ 12 (mod 17) b) 4x ≡ 11 (mod 19)

Q: solve the following linear programming problem using graphical method Max (Z)=80x+72y S. T: 5x+3y ≥…

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Q: Q-4: Let T: R³ a) Show that I is a linear transformation. b) Describe R(T). What is the dimension of…

A: The linear operator is T : ℝ3→ℝ3 defined by Txyz=x-y-z2z

Q: 3. Consider the Initial value problem ry' = y + r ln(r); y(1) = 2 (a) Estimate y(1.5) using Euler's…

A: b) Given: xy'=y+xln(x)⇒y'=yx+ln(x);y(1)=2 and h=0.25

Q: 1 1 5 0 2 1 EEPEN -1 -2 0 3 -1 -1 7 2 -4 1 - -

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Q: Find the arc length of the curve below on the given interval. y = In (x-√x² - 1), for 1 ≤x≤ √442…

A: Given y=lnx-x2-1, for 1≤x≤442   To Find: The arc length of the curve given on the given interval.

Q: N -10+ -30+ (x)+(x)=x too-

A: Graph of h(x)=f(x)+g(x) is given where f(x) is cosine function. To determine: The function g(x).

Q: 1=₁x-e³dx Obtain the numerical integral of the integral by dividing the integral into 5 equal parts…

A: Given: I=∫36x·e3xdxWe have to evaluate the integral using the Trapezoidal method and Simpson's…

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A: Introduction: The act of combining two or more items is known as addition. The process of computing…

Q: √√2 (5 (5x + 3y)dA where R is the parallelogram with vertices (0,0), (2,1), (-1,3), and (1,4). Use…

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Q: A study was made on the amount of converted sugar in a certain process at various temperatures. The…

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Q: Q.1: Solve the differential equation below; xy' + 4y = 8 x¹

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Q: Given the system C. dx dt dx, f. dt = 4x₁ - 1x₂ a. Write the above system in matrix form ie dx dt b.…

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Q: Which of the following is a potential function f for F(x, y, z) = (2x cos(yz). -x²z sin(yz) + 2yz?,…

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Q: 3. Apply Lagrange's interpolation formula, find In 9.2 with n=3 and the values below 9.5 10.0 11.0…

A: To find- Apply Lagrange's interpolation formula, find ln 9.2 with n = 3 and the values below X…

Q: p(x) = x(x-k) (x+k) is divided by (x-2k) is  3/4. Find the value of k. Hence, find the remainder…

A: We have p(x)=x(x-k) (x+k) Remainder theorem says that when a polynomial px is divided by x-a then…

Q: Show that the given differential equation 3x²y" + (2x² + 22² + ³) y y=0 has a regular singular point…

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Q: 1. Find the orthogonal trajectories of the given family of curves: Circles through the origin with…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: skla 8. What is the value of Fourier discrete function & [k] at k = 1?

A: To determine: The value of the Fourier discrete function δk at k=1.

Q: Locate the stationary point of the function z = 3x² + 4xy + 3y² (solve) Saddle point Maximum point O…

A: Sol  Correct option:- Maximum Point Explanation

Q: Let X be an inner product space. Then show that the projection theorem holds if and only if Riesz…

A: Given that: X=Inner product space. The objective is to show that the projection theorem holds if and…

Q: Given the scalar functionf (x, y) = 2xy, calculate the line integral along the ellipse curve+= 1…

A: To Evaluate: ∫CF·dr, where F(x,y)=2xy and the curve is  C: x29+y24=1.

Q: QUESTION 3 For a certain population the growth rate is dependent on the size of the population. The…

A: From the above details we have,

Q: 9. (a) Show that the functions r(t) = 3et+ 7e-t and y(t) = 3et+21e-t are solutions of the system I'…

A: Given: 9. a) x(t)=3et+7e-t and yt=3et+21e-t and a system, x'=2x-yy'=3x-2y satisfying the initial…

Q: 9. Let 2 be a bounded open subset of C, and y: → a holomorphic function. Prove that if there exists…

A: From the above details we get,

Q: Let F(x) = f(x5) and G(x) = (ƒ(x))5 . You also know that a¹ = 14, ƒ(a) = 3, ƒ'(a) = 8, ƒ' (a³) = 6…

A: Use the following formulae, to obtain the solution. Chain rule for differentiation:…

Q: Problem 2. To prepare for summer, Diffy E. Kew is trying out a new lemonade recipe. Through rigorous…

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Q: 1- ل + 27 - +f(x - x) w e dw

A: As per the question we are given an improper integral and we will evaluate it using the properties…

Q: Evaluate J₁ 1 E x² + y² + z² x² + y² +2²= 25 in the first octant. dV, where E lies between the…

A: Here we need to use spherical co ordinate system to find value of integral  Relation between…

Q: Question 1 (a) The following information was reported form the survey collected on customers'…

A: ANSWER (A): This is a non numerical data with categories as A, B, C, D. So, it is a categorical…

Q: 2. Consider the integral ² sir sin redr which can be computed exactly. a) Apply Romberg integration…

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Q: Q.5: Find a power series solution of the differential equation, at y(0.3); where the initial values,…

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Q: QUESTION 1 A group of researchers conduct a study about frost penetration in country X and come out…

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Q: Find vector-valued functions forming the boundaries of the region in the figure. Intervals are given…

A: given graph we have to find vector valued representation.

Q: 9. Evaluate the integral, where C is the above half of the circle = R from z₁ = 1 to z₂ = -1.

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Q: (a) Give the centre c and the radius r of S = B(0,5) B(3, 4). (b) Which of the following are neither…

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Q: (a) Show that every compact subset of M is bounded. (b) Show that every contraction map f: M→M is…

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Q: a) Find the Laplace transform of h(t)= cos 5t-3u (t-5) cost (1) Jutransfo 2133 Ordinc Lapl

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Q: 10. Evaluate the integral cz(z-1) where C is a simple closed curve in the positive direction that…

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Q: 13. Aij If for a square matrixes, [a] of even order (4) A is skew-symmetric (C) A is symmetric and…

A: Here we have given that aij=i2-j2 So, for all i=j  we have aii=0 that means all the diagonal…

Q: 2. Consider the integral ² si sin redr which can be computed exactly. a) Apply Romberg integration…

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Q: 1 If f(x) is a non-negative continuous function for all x, such that f(x) + + f(x+1/2) = 1,0 ≤ x ≤ -…

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Q: Examine the increasing and decreasing of each of the following sequences, whether they are bounded…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The elements of the quotient group (2/8). 12 (0,1,2,3,...,8) 1- 2- -208,-108,008,108,208,...) 3- 4-…

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Q: 1. Consider the function f(x, y) = {√x² + y² if x # (0,0) 0 if x = (0,0) Evaluate f(x, y) over the…

A: Thank you for the question. According to our guidelines we can answer only  first question and…

Q: Please give the steps that how obtain the effect asymptotical stabilization control law for the…

A: As per the question we are given a state space system as : ẋ = Ax + Bu y = Cx + Du And we have to…

Q: If R is a system satisfying all the conditions for a ring with unit element with possible exception…

A: To prove that the axiom a+b=b+a must hold in R and R is thus a ring

Q: Which of the following satisfies the statement f(x) is O(g(x)) when x5log(x+1) f(x) = +16x²? -5x3…

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Q: Use the matrices that you found in part (a) to show that the linear transformation f = kohog is…

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Q: Letr = (15462 37) and q = (2 4 5 6) be permutations in S7, written in cycle notation. What is the…

A: The given permutations are r=(1 5 4 6 2 3 7) , q=(2 4 5 6). To write: The second line of r in…