In this question, we seek to determine the area of a rectangular domain, R, with base on the x-axis and inscribed between the curve C:y=2 x and the circle of radius 2 centred in the origin, S:x²+ y² =4, and solve an optimisation problem related to it. The domain lies in the first quadrant. Let a be the x-coordinate of the top-left vertex of R and b the x-coordinate of the top-right vertex. a) By considering a line parallel to the x-axis and the vertices of R, or otherwise, find an equation relating the square of a and the square of b. We have that b^2= b) State the width, w, and height, h, of R as a function of a. We find that w = and h = c) State the area, A of R as a function of a: A(a) = d) The rectangular domain represents a flat garden whose cost in £ is given by C= a² + 3 b² +8 a. Find the maximum cost of the garden. The maximum cost is C= £49✓ Enter your approximate numerical answer rounding to the nearest pence. Does the most expensive garden correspond to the largest one? Justify your answer

Q: In a study conducted at Dartmouth College, mice with a particular type of cancerous tumor were…

A: In a study conducted at Dartmouth College, mice with a particular type of cancerous tumor were…

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A: Using the table of Laplace transformation, it can be written that: Ltn=n!sn+1.

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Q: 3 Find and sketch the graph of the domain of f (x, y)= 14x? +16у? - 64

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A: given,       hx=2x+2-8

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

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Q: A parabola has a focus of F(2,−0.5)F(2,−0.5)and a directrix of y=−1.5y=−1.5. P(x,y)P(x,y)represents…

A: Let (x, y) be any point on the parabola. So, the distance between (x, y) and the focus will be :