Example 7: Complete the following compositions. A translation (x,y) → (x+7, y + 2) followed by a counterclockwise rotation of 90°. The preimage is a triangle with points M(-2,-3), N(-4,-1), and R(-5,-5).

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Q: Prove that the following linear program is unbounded. max ( 2 +1X3 -3Xx₁ X₂ 4 +2X3 -1x₁ +2x1 X4 8 X5…

A: To Prove- Prove that the following linear program is unbounded. max ζ = 2 + x3 - 3x1x2 = 4 + 2x3 -…

Q: B/ Express f(x) = cos wx, - < x < π, as a Fourier series. Hence prove that 2w 2w 2w + + π(ω2 – 12)…

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Q: What is vector field and potential function? Sketch the gradient field of p(x, y) = x² + y² – k².

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Q: Let T: R3 → R3 be a linear trans formation such that T(1,1,1)=(2,0,-1),T(0,-1,2) = (-3,2,-1) and…

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Q: Consider the conditional/implication "If pancakes are fluffy and waffles are crunchy, then bread…

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Q: Which of the following represents the volume of the solid in the first octant bounded by the…

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Q: Which of the following series is divergent? ° 3n² 1+n² n=0 O n=0 n=0 8 4 n2n n=1 None of the given…

A: Solution :- Check each series for divergent :- 1. ∑n=0∞ 3n21+n2Apply the constant multiplication…

Q: 7. When a non-elementary integral A. is definite and continuous, it cannot be solved by any…

A: Introduction: There are two different types of integral. One is proper integral and another is…

Q: 10. Use Green's Theorem to evaluate the integral fe y dx + 2xy³ dy, where C is the square with…

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Q: 8. You expand a rectangular garden so the perimeter is now twice the perim- eter of the old garden.…

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Q: Which of the following sequence is divergent? 3- 2n²\ n² + 1 S ( 3 sinh n sin n °{2(#)} 0{-3.} None…

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Q: let 4 be a Hilbert space and s, and so be any two subset of H then (3) {o? ² = H (") SAS+ = {0} 9,…

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Q: Find all values of the full power. ASAP 2 (ei)√₂

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Q: 4. a) Prove that A i) V=I I+A 1+A ¡¡) fx+nh = Σx=0 (7) 4¹ fx.

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Q: A curve C is given parametrically by x = cos(t) and y = cos(2t), where -≤t≤ Find and equation in x…

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Q: Two cars are moving towards an intersection. One car is 150 meters north of the intersection and…

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Q: Question 2 (a) Find an orthonormal basis of the vector space P₂ of polynomials of degree at most 2…

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Q: 4. If G = (Z8,) then G has an element of order 5. *True *False

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Q: A chemist is carrying out laboratory experiments to verify the operation of a new pharmacy on a…

A: The population of bacteria is defined using the equation: N(t)=10t3-255t2+1800t+1000, where t is the…

Q: Evaluate the following integrals. ·[³ 1. 2x log 2x dr

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

Q: = M I = √√3-1² S₂3 2 √2-√√4-1²-y² 2y dz dy dr

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Q: Evaluate the path integral between the points A = (1,3) and B = (2,5) of: B *(x²y + 2y)dy, with y =…

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Q: your working. (b) For which real values of does each of the following series converge? Justify your…

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Q: Find the edge chromatic number of Kₙ when n is a positive integer.

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Q: 6. Maximizing the below profit function with respect to the constraint, evaluate if a solution…

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Q: What is the Maclaurin series representation of f(x) = 2*? Hint: exc

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Q: Let f(x) = x³ + 9x² - 21x + 20. (a) Use the definition of a derivative or the derivative rules to…

A: Note: We are entitled to solve only one question at a time and up to 3 sub-parts only. As the…

Q: Show that lim (x,y) → (0,0) 12 √16x +9y¹ 4x²+3y does not exist. Please show a complete solution.

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Q: B/ Express f(x) = cos wx, - < x < π, as a Fourier series. Hence prove that 2w 2w 2w + + π(ω2 – 12)…

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Q: 13 1 y = 1/2x² + ²x² 6x 1 √2 <x< 1 Curved segment rotated about the ox-axis.Calculate the area of…

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Q: Letr> 2. Show that sin² r - sin² 2 r-2 < 2. Justify your answer. Hint: Apply the Mean Value Theorem…

A: Let r&gt;2.   To Show: sin2 r-sin2 2r-2&lt;2.

Q: Find the inverse of the function on the given domain. f-1 (x) = f(x) = (x - 18)2, [18, ∞)

A: Inverse of function f(x)=(x-18)2 . In the interval [18, infinity) is  f-1(x)= 18+sqrt(x)

Q: H.w: Find the Fourier series for the following functions: and The function is odd or even? -T≤x≤0…

A: To find the Fourier series for the below function. fx=1+2xx    −π≤x≤01−2xx         0≤x≤π

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A: Given:  The diameter of the wheel is 24 meters. The wheel's bottom is 2 meter above from the ground.…

Q: Consider the function f(x, y) = ax – 2y + 1 where a is a positive number. S SR ax 2y + 1 dA = 45,…

A: A double integral involves the integral with respect to the product of any of two variables in x,y,…

Q: Consider the following system of equations. 2x1 + X2 + *3 = b1 X₁ - 3x₂ + 4x3 = ₂ -X1 + x3 = 3 (a)…

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Q: Given that C = C₁ U C₂ U C3, where C₁ is the line segment from (−1, −1) to (0, 0), C₂ is the line…

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Q: D Question 9 Set up but do not evaluate an integral that represents the volume of the solid of…

A: Sol:- The volume for solid of revolution between curves is the volume of object between a curve fx…

Q: Let H≤G & KG. Show that HnKH. Let H◄ G & K G and assume that Hn K = {e}. Show that if aeH & beK then…

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Q: Consider the following normal form of a game. K L M OF OD no dominant strategy (2,3) OE (3,2) (4,3)…

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Q: For all x E R, it is known that 1. Find the value of f(2022) (0). 2. Find the exact value of f(x) +∞…

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Q: b) Find the equation of the plane containing lines ₁ : x = 2+5t, y = 4+2t, z = -t and l₂: x=2-t₁y =…

A: We have to find the equation of the plane containing lines l1 : x=2+5t, y=4+2t, z=-t and l2 : x=2-t,…

Q: Find the Fourier transform of the following functions: (₁) f(t)= (11) "-(1+t), -12 t ≤0 t-1 04+ ²1 อ…

A: We have to find the Fourier transform of the given functions: (i) ft=-1+t-1&lt;t≤0t-10&lt;t≤10t&gt;1…