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- 7) The diameter of the base and the height of a closed right circular cylinder are measured,and measurements are known to have errors of at most 0.5 cm. If the diameter and height aretaken to be 4 cm and 8 cm, respectively, find bounds for the propagated error ina) the volume V of the cylinder, b) the surface area S of the cylinder.Determine the following for a q-curve with parameters κ = 6 and ν = 13. a. The q-value having area 0.05 to its right b. q0.01A circle with center at the origin and radius equal to a meets the axis of x at A and B.P(alpha) and Q(beta) are two points on the circle so that alpha-beta=2gamma,where gammais a constant.Find the locus of the point of intersection of AP and BQ.
- A rectangle is to be inscribed under the arch of the curve y = 4 cos (0.5x) from x = -π to x = π. What are the dimensions of the rectangle with largest area, and what is the largest area?Find the length of the graph of y = (1/2) cosh 2xfrom x = 0 to x = ln 25.A circle with center at the origin and radius equal to a meets the axis of x at A and B.P(alpha) and Q(beta) are two points on the circle so that alpha-beta=2gamma,where gamma is a constant.Find the locus of the point of intersection of AP and BQ.
- a polygon ABCDE is inscribed in a semi circle. The two points A and E at locations cos theta and -sin theta on the x-axis respectively, where 0<= theta < pi/2. As point C is fixed on the y-axis, all points except C shift positions where the value of theta changes. At a certain value of theta, it is found that the area of polygon equals to 41/50units square, and the length of AE equals to an irreducible fraction alpha/beta. What are the integers alpha and betaFind the areas of the regions . 1. Shared by the circle r = 2 and the cardioid r = 2(1 - cos u) 2. Shared by the cardioids r = 2(1 + cos u) and r = 2(1 - cos u)From the vertex (0, c) of the catenary y = c cosh(x/c) a line L is drawn perpendicular to the tangent to the catenary at point P. Prove that the length of L intercepted by the axes is equal to the ordinate y of the point P.