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(69) Why is it impossible to find the instantaneous rate of change of f(x)= x^2-9/x-3 at x=3? THE SLASH IS THE FRACTION SYMBOL.


why will f(x)= x/x^3-2x^2+5x have no zeros? ( THE SLASH IS A FRACTION SYMBOL, EVERYTHING BEFORE THE SLASH IS the nominator AND ANYTHING after the slash is the denominator. )


Using diagrams and the concept of elasticity of demand to support your answer, explain how both UK rail companies and airways go about filling seats in order to maximise revenue


A company is planning to bucketize



its data to improve the search



operation. The data is a sequence of



digits [0-9]. The bucket ID is



calculated as the sum of all the prime



digits in the data. The prime number



is a number that is divisible only by



itself and 1.



Write an algorithm to find the bucket



ID for the data as the sum of all



prime digits in the data.

A company is offering a special discount to its customers based on an algorithm two range values are fed to the algorithm and in return it will calculate the discount to offer to the customers the discount is calculated as the sum of all.the prime numbers

A 2.0kg mass fails 400cm.


(a) how much work was done on it by gravitational force?


(b) how much PEG did it lose?


(c) given that work is the transfer of energy where does that energy end up?

A 1200kg car going 30m/s applies its brakes and skids to rest. If the friction force between sliding tiresband pavement is 600N. How far does the car skids before coming tonrest.

A 500 kg roller coaster is pulled to the top of a hill 45 m high and arrives at the top with a zero speed.



a) how much work has done by the vhain to pull the car to the top?



b) how much potential energy does it have at the top?



c)What is the total energy of the system?



d) how much kinetic energy does it have at the bottom?



Consider an employee who does not receive employer-based health insurance and must divide her $1,000 per week in after-tax income between health insurance and “other goods.” In the graph below, draw this worker’s opportunity set if the price of health insurance is $200 per week and the price of “other goods” is $100 per week. On the same graph, draw this worker's opportunity set for the case where the employer agrees to give this employee $200 worth of health insurance per week (under current tax laws, this form of compensation is nontaxable).

Would this employee be better or worse off if, instead of the health insurance, the employer gave her a $200 per week raise that was taxable at a rate of 25 percent? Explain.



When purchasing bulk orders of​ batteries, a toy manufacturer uses this acceptance sampling​ plan: Randomly select and test 39 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 3 batteries do not meet specifications. A shipment contains 3000 ​batteries, and 1​% of them do not meet specifications. What is the probability that this whole shipment will be​ accepted? Will almost all such shipments be​ accepted, or will many be​ rejected?


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