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- The 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.A rectangle can be drawn in the first quadrant bounded by the curve y=8-x^3, the x- axis and the y-axis. determine thw dimensions (length and width) of the largest rectangle that can be drawnThe long run. A chair manufacturer hires its assembly-line labour for $18 an hour and calculates that the rental cost of its machinery is $6 per hour. Suppose that a chair can be produced using 4 hours of labour or machinery in any combination. The firm is currently using 1 hour of labour for every 3 hours of machine time. (Assume that labour is on the horizontal axis and capital is on the vertical axis). 3. Graphically illustrate your answer by drawing an isoquant, an isocost line for the current combination of labour and capital and an isocost line for the optimal combination of labour and capital. An isocost corresponding to the optimal combination of labour and capital is [a vertical line, a horizontal line, an upward sloping straight line, an upward sloping curve which is not a straight line, a downward sloping straight line, a downward sloping curve which is not a straight line, L-shaped] has slope [ ] at the optimal combination of inputs An isoquant…
- A closed rectangular box with faces parallel to the coordinate planes has one bottom corner at the origin and the opposite top corner in the first octant on the plane 5x+6y+z=1. What is the maximum volume of such a box? Volume=transcendental curve of #5 #6 and #7a. symmetryb. interceptsc. horizontal asymptoted. vertical asymptotee. regionf. tracing/curvearea bounded by the parabola x^2=4ay and a chord passing through its vertex show graph
- Application of derivative Optimization We are going to fence in a rectangular field that encloses 200 m2. If the cost of the material for of one pair of parallel sides is $3/m and cost of the material for the other pair of parallel sides is $8/m determine the dimensions of the field that will minimize the cost to build the fence around the field.Use 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?1) When cross-sections perpendicular to the x-axis are taken from the object whose base is bounded by the y = x² + 1_parabola, the coordinate axes and the line x = 1, a) squares, b) semicircles, ,,, with a diameter of the xy-plane are formed. Find the volumes by drawing the graphs of this object.
- XYZ is an isosceles triangle with base YZ. YZ=5cm; Height of triangle=10cm. A square is put into the triangle and 1 of its vertices is the midpoint of YZ. Maximum area of the square=?.A rectangular field as shown is to be bounded by a fence. Find thedimensions of the field with maximum area that can be enclosed with 1000 feet of fencing. (You do not need to fence on the side of river). Picture Is attached8. A water tank has a bowl shape formed by rotating the region bounded by y = x^2, x = 0 and y = 4 about the y axis. Therefore the height of the tank is 4 m and the radius at the top of the tank is 2 m. The tank is full of water. Find the amount of work needed to pump all of the water up out of the tank.