1. If R is the region in the first quadrant bounded by x-axis, 3x + y = 6 and y evaluate 3x, Jf 3y dA. R

Q: Consider the parabola C: 2-4 = -(x - 2)² on the az-plane. 1. Find the center-radius form of the…

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Q: True or False? 5. Let x and y be integers. If 5x − 7 is even, then x is odd. 6. Let x and y be real…

A: To find which of the above is true or false :-

Q: Which one is a correct symbolization of the following sentence in FOL? "Only happy poets like all…

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Q: B.) Convert the following function to standared form Min Z = 2x₂ + 5x3 S.t: x1 - x₂ ≥ 2 2x₁ + x₂ +…

A: Given  Min z= 2x2+5x3 x1-x2>=2 2x1+x2+6x3<=6 x1-x2+3x3=4 x1,x2,x3>=0

Q: the water in the tank? (Take = 3.14) 5. A water tank measuring 5 m long and 4 m wide contains water…

A: Let us consider a cuboid of length l , breadth b and height h then the volume of the cuboid is…

Q: Let n = pq, where p and q are distinct primes such that p = q = 3 (mod 4). Suppose a E Z+ with a <…

A: We use the properties and definitions of Jacobi symbols to solve this problem. The detailed solution…

Q: Find the volume of the solid generated by revolving the - area bounded by x² − 2kx − 3ky + k² = 0…

A: The given curves are  x2-2kx-3ky+k2=0                 …13x-3y+k=0                 …2 The given line…

Q: Question 6 A vector field is given by F(r) = z2+3+ yk, and a paraboloid is given by S = {(x, y, z) €…

A: Please see the attachment

Q: give the formal proof of validity

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Q: 22) (a) Show that the relation {(0,0), (1,1),(1,2), (2,1), (2,2), (3,3)} is an equivalence relation…

A: We can solve this using given information

Q: -2 11 5 100-10 The reduced row echelon form of the matrix A = Find a basis for the null space of A…

A: Note that null(A)=null(M), where M is in the echelon form of A  and the dimension of null(A) is…

Q: dy 2xy The general solution of + dx 1+x² A. y(1+x²) = c + tan-¹ x = c + tan-¹, X y B. 1+x² = 1…

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Q: Consider the set of Bernoulli trials where three items are selected at random from a manufacturing…

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Q: Q5- Find the Maclaurin series generated by the following function: f(x) = sinh(x)

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Q: 5- Find the Maclaurin series generated by the following function: f(x) = sinh(x)

A: Sol

Q: Let a and b be natural numbers and define d = gcd(a, b). Prove that alb iff d = a. For all sets A,…

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Q: 2) 2° +2¹+2²+...+ 2n = 2n+¹ -1 Remember: 2⁰=1

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Q: Determine whether the equation is exact. If it is exact, find the solution. 4 2e³ycosy + y² = c 4…

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Q: The Clausius-Clapyron equation relates the latent heat of vaporization to temperature and vapor…

A: Given the Clausius-Clapyron equation lnp=-∆HvRT+k---1. The units are R=8.3145 JK·mol, T with K, p…

Q: Solve the differential equation 3y 3y + 1 (sin ¹x)√1-3

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Q: Let u = (a11, a12, a13), v = = (a21, a22, a23), w = (a31, a32, a33) be three vectors in R³. Explain,…

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Q: my" + cy' + ky = F(t), y(0) = 0, y'(0) = 0 modeling the motion of a spring-mass-dashpot system…

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Q: A spinner is divided into five sections, labeled A, B, C, D, and E. Devon spins the spinner 50 times…

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Q: The value of the following = (2+ sin 2x3) Using the trapezoid integration dx method, knowing that n…

A: Sol

Q: i. g(x) Use the power series expansion of f(x) = 1 x)² 1 for x < 1 to find a power series expansion…

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Q: True or False? 3. The negation of the statement “For every ε > 0 there exists a δ > 0 such that if…

A: Since  you have posted a multiple  question according to guildlines I will solve first(Q3)…

Q: 11. Consider the function defined by f(x) = e-x². i. ii. iii. Using the Maclaurin series expansion…

A: The given problem is to find the Maclaurin series of given function and also evaluate the integral…

Q: Prove that sin²x x cos²x x = csc²x-cot²x 4csc²2x

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Q: Why is it necessary to get acquainted with the sigma notation's properties?

A: Yes, it is necessary to get aware of sigma properties . It help mathematics to improve itself.

Q: Q5) Minimize f(x) = (10x³ + 3x² + x + 5)²; using swann's method. Start with x,-3 and step size |A| =…

A: We know that Swann's method iteration formula is  xn+1=xn+2nh where h is step size Condition for…

Q: ` Use the Divergence Theorem to calculate the surface integral F-dS, where F = (2x, 3y, 0 S and S is…

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Q: 3 ²³₁²₁¹ [2³ (x + y)³] dz dy dx Z -4

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Q: (a) Evaluate the surface integral JL. TU xy ds where D is part of the plane x+y+3z = 3 that lies in…

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Q: find for y dy dx 3 x sinx √(x-1) (x²+1)

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Q: -) Determine the first six terms of the sequence defined by t₁ = -5 and t = 3t-1 + 8. 5, 23, -61,…

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Q: 8. a) Suppose (an) is a real sequence. Define the phrase, "(an) is a subsequence of (an)". b) Prove…

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Q: The function f(x) = x² + 1 is Bijection from R to R

A: This is a question from the function.

Q: A company distributes its products from four source to four retails stores. The supply capacities of…

A: According to guidelines we can solve only one problem.

Q: The investigator of a market reports the following data. Of 1000 persons questioned, 811 liked…

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Q: Find the determinant of the following elementary matrix by inspection. 1 0 0 0 1 0 E 0 0 -3 det(E) =…

A: I have given the answer in the next step. Hope you understand that

Q: 6. Which of the following is NOT an improper integral? ∞e-3r A. · S -dx 5 2x 5² x²-4 O A OB O C OD…

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Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 9(x² -…

A: Please see the attachment

Q: dC₁ = -k₁C₁ + k₂C₂ dt dCB dt B = k₁C₁-k₂C₁ Solve this ODE-IVP system in Excel up to 2 min with a…

A: We are given the following information.           k1=1 min-1k2=0.5 min-1CA0=1  (gmol/L)CB0=0…

Q: 2. Solve the initial value problem. State which rule you are using. Show each step of your…

A: Some of the properties of Laplace transformation…

Q: Describe geometrically all points P(x, y, z) that satisfy the given condition. X = 1

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Q: Which option, if any, would allow you to repay a loan in less time? decrease the regular payment…

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Q: Show complete work Prove the orthogonality of eigenvectors, and demonstrate it with a 2 DOF system…

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Q: -2 4 -2 -6-3 2 1 1. Let A = -3 8 2 -3 0 2 5 3 Answer the following. If you use technology, your…

A: Given matrix is: A=-24-2-42-6-31-382-30253Convert this matrix to row echelon form:Apply R2-&gt;R3+R1…

Q: Solve the following x²-x²-√√2x lime-21 x²-11x+18

A: Use L' Hospital Rule to evaluate the required limit as in next step.

Q: Let u = (a11, a12, a13), v = = (a21, a22, a23), w = (a31, a32, a33) be three vectors in R³. Explain,…

A: Here we use the orthogonal property.