A rectangle is to be inscribed in the ellipse (xb)^2+y^2=1, where b>0 is an unknown real...

A rectangle is to be inscribed in the ellipse (xb)^2+y^2=1, where b>0 is an unknown real number.

What should the dimensions of the rectangle be (in terms of b) to maximize its area? What is the maximum area (again, in terms of b)?

Expert Solution

milcah answered 1 year ago

Consider the IVPs: (A) y'+2y = 1, 0<t<1 , y(0)=2. (B) y' = y(1-y), 0<t<1 ,...

Consider the IVPs: (A) y'+2y = 1, 0<t<1 , y(0)=2. (B) y' = y(1-y), 0<t<1 , y(0)=1/2. 1. For each one, do the following: a. Find the exact solution y(t) and evaluate it at t=1. b. Apply Euler's method with Δt=1/4 to find Y4 ≈ y(1). Make a table of tn, Yn for n=0,1,2,3,4. c. Find the error at t=1. 2. Euler's method is obtained by approximating y'(tn) by a forward finite difference. Use the backward difference approximation to y'(tn+1)...

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Let Q1=y(1.1), Q2=y(1.2), Q3=y(1.3), where y=y(x) solves... 1) y'''+2y''-5y'- 6y=4x^2 where y(0)=1, y'(0)=2, y''(0)=3 2) y'''- 6y''+11y'- 6y=6e^(4x) where y(0)=4, y'(0)=10, y''(0)=30 3) y''- 6y'+9y=4e^(3x) ln(x) where y(1)=, y'(1)=2 Please show all steps and thank you!!!

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How to transform x^2+xy+y^2+4x+2y=0 into the standard for of an ellipse and finding the vertices of...

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Consider the parabolas y=x^2 and y=a(x-b)^2+c, where a,b,c are all real numbers (a) Derive an equation...

Consider the parabolas y=x^2 and y=a(x-b)^2+c, where a,b,c are all real numbers (a) Derive an equation for a line tangent to both of these parabolas (show all steps with a proof, assuming that such a line exists) (b) Assume that the doubly-tangent line has an equation y+Ax+B. Find an example of values of a,b,c (other than the ones given here) such that A,B ∈ Z

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A rectangle is to be inscribed in the ellipse (xb)^2+y^2=1, where b>0 is an unknown real...

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Expert Solution

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