A rectangular block of metal with a square cross-section has a total surface area of 250 cm². Find the maximum volume of the block of metal.A cycloid has parametric equations given by: x = 5θsinθ and y = 5(1cosθ).Evaluate dx when θ = 1.5 radians. Give answers correct to decimal places.Determine the equation of (a) the tangent; and (b) the normal, drawn to an ellipse x^2/4cos^2θ y^2/sin^2θ = 1.Determine expressions for dz/dy for each of the following functions:(a) z = sy - cos(x)(b) z =
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