- Let A(p², - p), B(q², q), C(r², – r) be the vertices of triangle ABC. A parallelogram AFDE is drawn with D, E, and F on the line segments BC, CA, and AB, respectively. Using calculus, show that the maximum area of such a parallelogram is = |(p+q)(q+r)(p_r) |.

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A: here we will use mid point rule to find approximate value of integral

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A: As per the guidelines of Bartleby once max three subparts can be answered, please repost other…

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Q: en prove that there exists a rational numb =k. Hence, prove that the numbers √2,

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Q: x₁ + x₂ + +x. Prove that -x₁)(1+x₂)... (1+x) ≤1+S+ ... S² S³ + 2! 3! +...+ uS - n!

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Q: use integration by parts to evaluate the integral 2xcos (3x) dx

A: The given problem is to evaluate the given integral of 2xcos(3x) by using integration by parts.

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A: Type-A Type-B Requirement  Oats 2 7 70 Corn 5 3 75 Store Capacity  30 20

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Q: 3Q. Find a series solution around xo = 0 for the following differential equation. y" - 4y = 0

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A: We have used Mathematical Induction to prove the statement (Can be found in next step);

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Q: Consider the following differential equation. (2x - 1) dx + (7y + 4) dy = 0 Let M = 2x - 1 and N =…

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Q: Graph each function using degrees. 3) y sin 0-2 90° 180° 2709 360° 450° 540 4) y = cos 0 +2 90° 180°…

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Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

A: Given That : F=4x+exsinyi^+5x+excosyj^ C: Right-hand loop of the lemniscate r2=cos2θ  To Find :…

Q: 4. x and y are two positive integers. (x,y) = 5, Icm (x,y) = 200 and 15, find x and y. gcd x - y =

A: Given that     gcd(x,y) = 5 ;   lcm(x,y) = 200   and  x-y = 15 Formula :     xy =…

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Q: 2. (Section 17.6) Given that 7 = 2yî – rĵ + rzk, evaluate [[F. ds where S is the part of z = 3+y…

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Q: Find the chromatic index of each graph?

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Q: Prove each of the following statements using mathematical induction. (b) n Prove that for any…

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