Calculus Answers

The golf ball manufacturer has developed a profit model that depends on the number x of golf balls 

sold per month(measured in thousands),and the number of hours per month of advertising y, according 

to the function

𝑧 = 𝑓(𝑥, 𝑦) = 48𝑥 + 96𝑦 − 𝑥

2 − 2𝑥𝑦 − 9𝑦

2

,

Where z is measured in thousands of dollars .The budgetary constraint function relating the cost of the 

production of thousands golf balls and advertising units is given by 

20𝑥 + 4𝑦 = 216,

Find the values of x and y that maximize profit, and find the maximum profit

You are building the Great Pyramids of PCA, and you need to know how much stone you need to lay out. You determine that the 5th layer of the pyramid requires 720 ft of stone, and the 21st layer requires 600 ft of stone. Each successive layer of the pyramid differs by a constant length. How many feet of stone you need to build the first 15 layers?

Find the area of the largest isosceles triangle that can be inscribed in a circle of radius 6 inches.

Find the area of the largest rectangle with sides parallel to the coordinate axes which can be inscribed in the bounded by the two parabolas y=26-x^2 and y=x^2+2

Find the dydx of y=sin-12x-√1-4x2

if a = 15 80° and b = 12i + 16j what is the magnitude of a - b

Find the centre of gravity of a thin sheet with density δ(x, y) = y, bounded by the 

curves

y = 4x² and x = 4

Determine the volume of the solid formed when the region enclosed by the curve y=√x, the x-axis, and the line x = 4, is revolved about the line x = 4.

Find the centroid of the solid generated if the region bounded by y = 2- x^2, x=0, and y=0 is revolved about the y-axis.