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April 22nd, 2011, 09:28 PM   #1
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Some advanced precalculus questions

I got a bunch of homework. But these are the hardest. Others I could have some clues to solve, but for these I'm clueless. Please help

1) If f(x)=3sin x+4sin(x-3) what is the amplitude and period (p) of f(x)?
A) a= 1.114, p = 6.283
B) a= 1.114, p = 3.141
C) a =2.28, p= 3.141
D) a=7, p = 6.283
E) a= 7, p= 9.425

2)A Ferris wheel rider's height above the ground is given by the function h(t)= 20+18 cos [ (pi/4)* (t-3)], where h is measured in feet and t in seconds. How much time is required for the Ferris wheel to complete 1 full revolution?
A) 3 secs
B) 8 secs
C) 18 secs
D) 20 secs
E) 38 secs

3) The graph of the daily temperature at noon of a city is modeled by T= -25 cos [ (2pi/365) * (t-30)] +70, where T represents the temperature in degrees Fareinheit and t represents the day of 365- day year. Whats the range of the temperature from low to high during the year?
A) 25-> 70 Celsius
B) 30-95 Celsius
c) 45-95 Celsius
D) 30-90 Celsius
E) 35-95 Celsius

4) If f(x)= sin x* sin (-x), then which is the range of f(x)?
A) [0,1]
B) [-1,0]
C) [-1,1]
D) [-1,0)
E) (0,1]

5) Function D (t) = (4t)/ (0.01t square+5.1). Given the concentration, D, of a drug in bloodstream where D is measured in micrograms per milliliter and t is minutes from the time the drug is taken. What's the maximum concentration of the drug found in bloodstream at any time?
A) 0.01 micrograms/ milliliters
B) 4 micrograms/ milliliters
C) 5.1 micrograms/ milliliters
D) 8.856 micrograms/ milliliters
E) 22.583 micrograms/ milliliters
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April 23rd, 2011, 04:36 AM   #2
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Re: Some advanced precalculus questions

1.) We may use the identity

Thus, amplitude is

Period is

2.) The period is

3.) The range in degrees Fahrenheit is

4.) range is [-1,0]

5.) Graphing shows D is the only answer which makes sense. I would use a technique from calculus to find the maximum is .
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April 23rd, 2011, 04:52 AM   #3
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Re: Some advanced precalculus questions

Hello, belly!

Quote:

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MarkFL "eyeballed" the problem! . . . Great1
[color=beige] .[/color]
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April 23rd, 2011, 05:31 AM   #4
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Re: Some advanced precalculus questions

Hello again, belly!

Quote:



[color=beige]. . [/color]



[color=beige]. . [/color]

Since this is [color=blue]pre[/color]-Calculus, MarkFL has the best approach . . . graphing.


If we are allowed to use Calculus, we can directly determine the maximum concentration.








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