A 1125 ft3 open-top rectangular tank with a square base x ft on a side and y ft deep is to be built with its top flush with the ground to catch runoff water. The costs associated with the tank involve not only the material from which the tank is made but also an excavation charge proportional to the product xy. a. If the total cost is c = 5(x2 + 4xy) + 10xy, what values of x and y will minimize it? b. Give a possible scenario for the cost function in part (a).

Q: The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its…

A:

Q: Use the photo attached to answer the following question, 1.Using the centre of gravity location…

A: The Center of Gravity Method is an approach that seeks to compute geographic co ordinates for a…

Q: 7. A box with an open top is to be constructed from a rectangular piece of cardboard 1 m long by 0.5…

A: Let x be the length of each side of the square  that is cut Therefore the height of the rectangular…

Q: 2. Find the root of the following equation through the different methods, f(x) = x^3 − x − 1 a.…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: Water is being pumped into an inverted (point down) conical tank at a constant rate. The tank has…

A: Let h be the height of the water surface Let r be the radius of the water surface Volume of a cone V…

Q: Jibby needs to make the edge of a box in the shape of a cuboid using a piece of wire. The…

A:

Q: man is filling up an inverted pyramidal tank with water at a constant rate. The tank has the…

A: Let the length of poster ABCD =x cmBreadth of poster =y cmTop margin=2.5cmBottom margin=1.5cmBoth…

Q: 2.Let be a company whose total revenue and total costs, in dollars, are given respectively by: R(q)…

A:

Q: Profit equals revenue minus cost: P=R – C.Use this equation to find the marginal profit, P' from the…

A: Simply  Apply the formula P=R-C Then diffrentiat this equation with respect to x Finally we got…

Q: In the following problem: Determine the dimensions of the rectangle with a diagonal of 15 cm and the…

A:

Q: You are manufacturing a can which is a perfect cylinder. The ideal volume of the can is 375 cm3 .…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.