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1. The demand and cost functions for a product are p(x) = 130 - 0.01x and C(x) = 30x + 1100, where x is the number of units produced weekly. If the manufacturer decides to increase production by 70 units per week, find the rate at which profit is changing with respect to time when the weekly production is 3600 units.
2. A rocket travels vertically at a speed of 500 km/hr. The rocket is tracked through a telescope by an observer located 18 km from the launching pad. Find the rate at which the angle between the telescope and the ground is increasing 3 min after lift-off.
3. A boat is pulled in to a dock by a rope with one end attached to the front of the boat and the other end passing through a ring attached to the dock at a point 6 ft higher than the front of the boat. The rope is being pulled through the ring at the rate of 0.4 ft/sec. How fast is the boat approaching the dock when 10 ft of rope is out?
One property of rational numbers is that they are dense, that is, between any two rational numbers is another rational number. Given two arbitrary rational numbers, show how you could find another rational number between them.
a kite is flying horizontally at a constant height of 100 ft above the girl flying the kite. at a certain instant, the angle whichthe string makes with the girl is 30 degrees and decreasing. if the string is paying out at 16 ft/s, how fast is the ..
What would happen (other things equal) to a confidence interval if you calculated a 99 percent confidence interval rather than a 95 percent confidence interval?
question you are given two points on a circle. is it possible to find an equation of the circle? is it possible if you
a steep mountain is inclined 79 degrees to the horizontal and rises 3100 ft. above the surrounding plain. a cable car is to be installed from a point 900ft from the base of the mountain. find the shortest length of cable needed?
A company wishes to manufacture a box with a volume of 56 cubic feet that is open on top and is twice as long as it is wide. Find the width of the box that can be produced using the minimum amount of material.
What uniform acceleration will bring an automobile running at 40 mi/hr, to rest in 120 ft? What time will be required?
Your task is to design a rectangular industrial warehouse consisting of three separate spaces of equal size as in Figure. Which dimensions maximize the area of the warehouse? What is the area of each compartment in this case?
You have scores of 99, 93 and 90 on the first 3 tests. You must make a total of 360 in order to get an A. What scores on the last test will give you an A?
How long does it take to reach 60% of the terminal velocity? (Round your answer to two decimal places.)
List all the elements of X that are less than 30 - the set X of all binary strings having the same number of O's and 1's is defined
An experimental drug is administered to 50 randomly selected individual, with the number if individuals responding favorably recorded.
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