Math Answers

A single-lane street 10 ft wide goes through a semicircular tunnel with radius 9 ft. How high is the tunnel at the edge of each lane? Roun off to 2 decimal places.

1. Find the derivative of the following functions:

a. 𝑓(𝑥) = tan^-1x+cotx / 5cscx

 b. 𝑦=3 −ln(2𝑥+1)

c. 𝑔(𝑥)=𝑥𝑒^x−sin𝑥ln(5𝑥)

Find the equation of the line tangent to the circle with the center at (-1,1) and point of tangency at (-1,3).

If A(u) is a differentiable vector function of u and ||A(u)||=1 , prove that dAdu is perpendicular to A .

Show that if B>0, then the graph of x²+Bxy=F, is a hyperbola if F≠0, and two intersecting lines if F=0.

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?

Drawing a Card. If one card is drawn from a deck, find the probability of getting these results getting a king

Drawing a Card. If one card is drawn from a deck, find the probability of getting these results Getting a queen

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

A copper hot -water tank is in the form of a cylinder with a hemispherical cap and stands on a flat base . The internal diameter of the cylinder is 525 mm and the overall internal height is 1200 mm .

Calculate : (a) the volume of the tank in m ^ 3 (b) the capacity of the tank in litres