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Consider the sequence given by a1 = 1, an = an-1 +(2n- 3). Can a technique from this chapter be used to find a closed form? Write out the first several terms of the sequence. Can you intuit a closed form based on the terms of the sequence? (Hint: ) Find a closed form for this recurrence and use induction to prove that the closed form is correct.
A poster is to have 150 square inches of printed area. If we want a 2 inch margin at the top, and 1 inch margins at the bottom and sides, what dimensions use the smallest amount of paper.
find the probability that, in a random sample of 20 individuals:
This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. You must complete the exam individually. Neither collaboration nor consultation with others is allowed.
What is the variance of the sum of the numbers that come up?
she suggests building fences described by y=4x2 and y=x2+5. Farmer Jones thinks this would be much harder than just building an enclosure with straight sides, but he wants to please his wife. What is the area of the enclosed region?
Define a vector field as and define the path C as the path graphed below lying in the x-y plane starting at x point (x,y,z) = (-2,0,0) and ending a (4,2,0).
Estimate the instantaneous rate of change of fuel consumption with respect to speed - Researchers at a major car company have found a function that relates gasoline consumption to speed for a particular model of car.
use Euler's Method with h=0.01 to approximate y(0.12)for the initial value problem dy/dx = e^-xy, y(0)=1
(a) Write an equation in x and y for the number of gallons of gas sold. (b) Write an equation in x and y for the amount of money received.
The manager of a grocery store wants to determine whether the amount of milk contained in 2-litre cans actually averages 2 litres as advertised. State the null and the alternative hypotheses. Which kind of test you will use to prove it?
Use Gauss's law to find the charge enclosed by the cube with vertices {(+/-)1,(+/-)1,(+/-)1} if the electric field is E(x,y,z) = 4xi+2yj+1zk
Fifty-six dog biscuits are to be given to ten pets. Each pet is either a cat or a dog. Each dog is to be given six biscuits and each cat is to be given five biscuits. How many dogd are there?
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