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A swimming pool is to be drained for cleaning. The quantity of Q of water (in gallons) in the pool at any given time is a function of the amount of time t (in minutes) which has elapsed since the drain was opened. the function is: Q(t)= 10(20-t)3
find Qβ(t)=
what is the rate of change of the quantity of water in the pool exactly 10 minutes after the drain is opened? (labeled units)
what is the average rate of change of the quantity of water during the first 10 minutes after the drain is open?
how long will it take to drain the pool completely? (labeled units)
If A(u) is a differentiable vector function of u and ||A(u)||=1 , prove that dA/du is perpendicular to A
A 13 ft ladder is leaning against a wall. If the top of the
ladder slips down the wall at a rate of 2 ft/s, how fast will
the foot be moving away from the wall when the top is 5 ft
above the ground?
A town has a population of 5000 and grows at 4% every year the initial population is 5000 find growth model and determine population after 3years
Currently the sowing of wheat is taking place in Pakistan till December, the harvesting season will
begin in March. So, the farmers wants to build a silo in the form of cylinder to keep the wheat inside
the silo after harvesting. For this purpose, they have to built silo of different sizes having 2000 cubic
units and 4000 cubic units. Moreover, the top of the cylinder is hemi-sphere. The cost of construction
of per unit surface area is thrice as great for the hemisphere as it is for the cylindrical sidewall.
Determine the dimensions to be used and cost of construction is to be kept to a minimum. Neglect the
thickness of the silo and waste in construction. Finally, use MATLAB to write a program which will
provide you the optimal dimensions subject to the constraint of cost. The program will take dimensions
of the Silo as input and return the cost and quantity of each size.
1. Find the derivative of the following functions:
a. π(π₯) = tan^-1x+cotx / 5cscx
Β b. π¦=3 βln(2π₯+1)
c. π(π₯)=π₯π^xβsinπ₯ln(5π₯)
If A(u) is a differentiable vector function of u and ||A(u)||=1 , prove that dAdu is perpendicular to A .
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 182ππ2 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 182ππ2. 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 π₯π¦ plane bounded by the curves π¦ = π₯
2 and
π¦ = 4π₯ β π₯
2
.
