Calculus Answers

A local pizzeria has acquired the services of your software house to help them with optimal use of their resources. The pizzeria sells slices of pizza, which are triangles take surface area of the triangular box as input and provide maximum volume as output. One additional requirement is that the base of the prism (triangular box) is a right isosceles triangle. To test your code the company has asked you to use 182𝑐𝑚2 as the surface area.

Sometimes the company knows their volume requirement and thus would want to know the surface area that will result in the desired volume. For this scenario, the company wants you to use the volume obtained from first case as input, the program should thus provide the dimensions and surface area that will result in the required volume; the answer of surface area should be equal to 182𝑐𝑚2. Furthermore, if the material cost is $5 per unit length, and the budget of the company is $2 million, how many triangular boxes will the company be able to make?

At a unit price of 16,000 the demand of a product is 300 units and at a price of 48000 the demand is 100 units.at a unit price of 30000 the supply is 550 units and at a unit price of 50000 the supply is 650 units.determine the equilibrium price and quantity

Find by double integration the area of the region in 𝑥𝑦 plane bounded by the curves 𝑦 = 𝑥

2 and

𝑦 = 4𝑥 − 𝑥

2

.

.Find the average value of 𝑓(𝑥, 𝑦) = 𝑥

2𝑦 over the region 𝑅 which is a rectangle with vertices

(−1, 0), (−1, 5), (1, 5), (1, 0).

find inverse laplace transorm : se^-2s/(s^2 + pi^2)

∫ ∫ 𝑥𝑦𝑑𝑥𝑑𝑦 2𝑦

𝑦

2

find laplace transform : sin wt (0 < t< pi/w)

Find an approximate value of the double integral below where 𝑅 is the rectangular region having

vertices (−1, 1) and (2, 3). Take a partition of 𝑅 formed by the lines 𝑥 = 0, 𝑥 = 1, and 𝑦 = 2, and take (𝑢𝑖

, 𝑣𝑖) at the

center of the 𝑖th sub region.

∬(3𝑦 − 2𝑥

2)𝑑𝐴

𝑅

find laplace transform : 4u(t-pi) cost

fine laplace transform : e^-2t u(t-3)