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1. Find an equation of the tangent line to the curve y = x√x that is parallel to the line y =1 + 3x.
2. The gas law for an ideal gas at absolute temperature T (in degrees kelvin), pressure P (in atmospheres), and volume V (in liters) is PV = nRT, where n is the number of moles of the gas and R = 0.0821 is the gas constant (in units of L · atm/(mol · K)). Suppose that, at a certain instant, P = 10 atm and is decreasing at a rate of 0.5 atm/min and V = 20 L and is increasing at a rate of 0.2 L/min. Find the rate of change of T with respect to time at that instant if n = 10 mol. What are the units of this rate of change?
Find the temperature at 9:01 A.M.,at 9:08 A.M.,and at 9:20 A.m.
Discuss marx's theory of history. What is the driving force behind his idea of the coming revolution?
The bucket is filled with 45 pounds of water and is pulled up at a rate of 1.9 feet per second, but water leaks out of a hole in the bucket at a rate of 0.1 pounds per second. Find the work done pulling the bucket to the top of the well. Your answ..
Let R be the region bounded by the curves f(x) = ln(x+3) +2 and g(x) = x^2 - 8x + 18. Using the washer method, find the volume of the shape which is formed if R is rotated around the x- axis.
the national unemployment rate in a recent month was 4.9 percent. you think the rate may be different in your city so
Show that the binary expansion of a positive integer can be obtained from its hexadecimal expansion by translating each hexadecimal digit into a block of four binary digits.
Mortgages and Taxes Assignment (Total 40 Points) Question 1: (20 Points) a) You are purchasing a business building valued at $225,000. You can find a mortgage at 5% if you can put 20% down. You believe your business can support a $1,000 a month mortg..
How many pizzas must be sold to break even (i.e., you experience neither a profit nor a loss)? Interpret your result.
A beach ball has a radius of 12 in.. How much air will the beach ball hold? (leave your answer in terms of π)
A sociologist recently conducted a survey of citizens over 60 years of age who have net worths too high to qualify for Medicaid but have no private health insurance.
The number of new contributors to a public radio station's annual fund drive over the last ten years is. Develop a trend equation for this information, and use it to predict next year's number of new contributors.
Find the future value of an annuity of payments of $700, made at the beginning of each month, for 12 years in an account that pays 12% compounded monthly.
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