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- Volume of Solid of a Revolution Show full solution and graph. Thanks! y = 2x - x^2, y = x; About line x = 1A cylindrical can with no top is to be constructed for 20 pesos. The cost of the material used for the bottom is 2 pesos per square inch and the cost of the material used for the curved side is 3 pesos per square inch A. Express the volume of the can as a function of its radius B. What are the dimensions that yield a maximum volumeUse Application of Derivatives A wire of length L is to be cut into two pieces, one to form a square and the other to form an equilateral triangle. How should the wire be divided to maximize or to minimize the sum of the areas of the square and triangle?
- The sides of square are initially 5 inches in length and increase at a constant rate of 3 inches per second.One corner of square moves along a line L at a speed of 2 inches per second for 5 second.During this time the square makes one complete revolution L, revolving at a constant rate and remaining always perpendicular to L. explain how carefully how to compute volume of solid generated by square.Carry out the computation you describe.Two curves are orthogonal if their tangents are perpendicular at each point of intersection. Show that the given families of curve are orthogonal trajectories of each other; that is, every curve in one family is orthogonal to every curve in the other family. Sketch both families of curves on the same axes. x^2 + y^2 = r^2, ax +by = 0A 500 gallon tank is filled with gasoline containing 10 pounds of a seasonal additive. A gasoline mixture containing 0.02 pounds of additive per gallon is added to the tank at the rate of 50 gallons per minute. The gasoline solution in the tank is continuously and thoroughly mixed and drained out at the same rate of 50 gallons per minute. How many points of additive are in the tank 30 minutes into the operation.
- non homogeneous equationThe area of the region is bounded by the x-axis, the curve y = 6x – x2, the line x – 1 = 0 and the line x = 4. 3. Find the ordinate of the vertex of the curve y = 6x – x2. Find the area of the region. Find the distance of the centroid of the area from the y-axis.Numerical Integration (Trapezoidal)
- Solid of revolution Give your solution about the intersection points.Two curves are orthogonal if their tangent lines areperpendicular at each point of intersection. Show that the givenfamilies of curves are orthogonal trajectories of each other,that is, every curve in one family is orthogonal to every curvein the other family. Sketch both families of curves on the same axes. x 2+ y 2= ax , x 2+ y 2 =byApply Euler’s semi-linear method (no other method) steps - complementary homogeneous steps - Variation of Parameters steps - Euler’s Method
