20121 calc dei adrian.jarriagam.tarea3p1respuestas

8/3/2019 20121 Calc DeI Adrian.jarriagam.tarea3p1RESPUESTAS

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ARRIAGA MORENO JANAI 20121 Calc DeI Adrian 1FV2WeBWorK assignment number Tarea3p1 is due : 09/05/2011 at 11:55am CDT.

The

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for the course contains the syllabus, grading policy and other information.

This file is /conf/snippets/setHeader.pg you can use it as a model for creating files which introduce each problem set.

The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are making

some kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you are

having trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TAs or your professor for

help. Dont spend a lot of time guessing its not very efficient or effective.

Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers,

you can if you wish enter elementary expressions such as 2 3 instead of 8, sin(3 pi/2)instead of -1, e (ln(2)) instead of 2,(2 + tan(3)) (4 sin(5))67/8 instead of 27620.3413, etc. Heres the list of the functions which WeBWorK understands.

You can use the Feedback button on each problem page to send e-mail to the professors.

1. (1 pt) Let

f(x) = 10

x2, x

0

f1(x) =Correct Answers:

(10 - x)(1/2)

2. (1 pt) Let

f(x) =1

3x + 6, 3x 8

The domain of f1 is the interval [A,B]where A = and B =

Correct Answers:

5 8.66666666666667

3. (1 pt) Let

f(x) = 2 + 5x + 3ex

f1(5) =Correct Answers:

0

4. (1 pt) Match the functions with their graphs. Enter the

letter of the graph below which corresponds to the function.

1. f(x) =5x2. f(x) = 5x3

3. f(x) = 5x+144. f(x) = 5x

5. f(x) = 5x

A.

B.

C.

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D.

E.

Correct Answers:

A D E C B

5. (1 pt) For the function f(x) = 9x, calculate the followingfunction values:

f(3) =f(1) =f(0) =f(1) =f(3) =

Correct Answers:

0.00137174211248285 0.111111111111111 1 9 729

6. (1 pt) The graph of the function f(x) = 5x 9 can beobtained from the graph of g(x) = 5x by one of the followingactions:

(a) shifting the graph ofg(x) to the right 9 units;(b) shifting the graph ofg(x) to the left 9 units;(c) shifting the graph ofg(x) upward 9 units;(d) shifting the graph ofg(x) downward 9 units;(e) reflecting the graph ofg(x) in the x-axis;(f) reflecting the graph ofg(x) in the y-axis;Your answer is (input a, b, c, d, e, or f)

Is the domain of the function f(x) still (,)?Your answer is (input Yes or No)

The range of the function f(x) is (A,),the value ofA is

Correct Answers:

d Yes -9

7. (1 pt) The number of bacteria in a culture is given by thefunction

n(t) = 935e0.4t

where t is measured in hours.

(a) What is the relative rate of growth of this bacterium popula-

tion?

Your answer is percent

(b) What is the initial population of the culture (at t=0)?

Your answer is

(c) How many bacteria will the culture contain at time t=5?

Your answer is

Correct Answers:

40 935 6908.76745250016

8. (1 pt) The population of the world in 1987 was 5 bil-

lion and the relative growth rate was estimated at 2 percent per

year. Assuming that the world population follows an exponen-

tial growth model, find the projected world population in 1995.

Your answer is billion

Correct Answers:

5.867554354959059. (1 pt) The graph of the function f(x) = log3(x

2) can be

obtained from the graph ofg(x) = log3x by one of the followingactions:

(a) shifting the graph ofg(x) to the right 2 units;(b) shifting the graph ofg(x) to the left 2 units;(c) shifting the graph ofg(x) upward 2 units;(d) shifting the graph ofg(x) downward 2 units;Your answer is (input a, b, c, or d)

The domain of the function f(x) is .Note: Enter your answer using interval notation.

The range of the function f(x) is .Note: Enter your answer using interval notation.

The x-intercept of the function f(x) is .The vertical asymptote of the function f(x) has equation:

.

Correct Answers:

a (2,infinity) (-infinity,infinity) (3,0) x=2

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1. f(x) = ln(x)2. f(x) = ln(x)3. f(x) = 2 + lnx4. f(x) = ln(x2)5. f(x) = lnx

A.

B.

C.

D.

E.

Correct Answers:

C D A E B

11. (1 pt) If ln a = 2, ln b = 3, and ln c = 5, evaluate thefollowing:

(a) ln a2

b4c1

=

(b) ln

b1c2a2 =

(c)ln

a4b2

ln(bc)3=

(d) (ln c2)

lna

b3

4=

Correct Answers:

-11 -1.5 -0.0833333333333333 0.0041649312786339

12. (1 pt) Evaluate the following expressions. Your answers

must be exact and in simplest form.

(a) log4

1256

=

(b) log6 1 =

(c) log6

7776 =3


4/7

(d) 8log8 10 =Correct Answers:

-4 0 2.5 10

13. (1 pt) Evaluate the following expressions. Your answersmust be exact and in simplest form.

(a) ln e3 =

(b) eln2 =

(c) eln

2 =

(d) ln(1/e2) =Correct Answers:

3 2 1.4142135623731 -2

14. (1 pt) Simplify the following expressions. Your answers

must be exact and in simplest form.

(a) log3 39x10 =

(b) 10log10(210q) =

(c) log5 15625k =

(d) 129log12 55log12 9 =Correct Answers:

9*x +{-10} 2 +-10*q (6/1)*k 33.0763433758404

15. (1 pt) The domain of the function g(x) = loga(x29) is

(, ) and ( , ).

Correct Answers:

-3 3

16. (1 pt) Use the Laws of logarithms to rewrite the expres-

sion

log

x10y16

z19

in a form with no logarithm of a product, quotient or power.

After rewriting we have

log

x10y16

z19

= A log(x) +B log(y) +Clog(z)

with

A =B =and

C=

Correct Answers:

10 16 -19

17. (1 pt) Use the Laws of logarithms to rewrite the expres-

sion

ln

x18

y16

z20

in a form with no logarithm of a product, quotient or power.

After rewriting we have

lnx18y16

z20= A ln(x) +B ln(y) +Cln(z)

with the constant

A =the constant

B =and the constant

C=

Correct Answers:

18 8

-10

18. (1 pt) Rewrite the expression

3logx3log(x2 + 1) + 3log(x1)as a single logarithm logA. Then the function

A =

Correct Answers:

x**3*(x-1)**3/(x**2+1)**3

19. (1 pt) Solve for x:

275x8 =

1

81

5x7

x =

Correct Answers:

1.48571428571429

4


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log2x + log2(x + 2) = log2 6

x =

Correct Answers:

1.6457513110645921. (1 pt) Solve for x:

log (x5) = (log x)2

Note, there are 2 solutions, A and B, where A < B.A =

B =

Correct Answers:

1 100000


109x6 = 44x2

x = .Correct Answers:

0.72755682732782723. (1 pt) At the beginning of an experiment, a scientist has

232 grams of radioactive goo. After 180 minutes, her sample

has decayed to 14.5 grams.

What is the half-life of the goo in minutes?

Find a formula for G(t), the amount of goo remaining at time t.G(t) =

How many grams of goo will remain after 68 minutes?

Correct Answers:

45 232*2**(-t/45) 81.3950911157599

24. (1 pt) The doubling period of a baterial population is10 minutes. At time t = 100 minutes, the baterial populationwas 50000. What was the initial population at time t = 0?

Find the size of the baterial population after 4 hours.Correct Answers:

48.828125 819200000

25. (1 pt) Students in a fifth-grade class were given an exam.

During the next 2 years, the same students were retested several

times. The average score was given by the model

f(t) = 9515log10(t+ 1), 0 t 24where t is the time in months.

(a) What is the average score on the original exam?

(b) What was the average score after 6 months?

(c) What was the average score after 18 months?

Correct Answers:

95 95-15 *logten(6+1) 95-15 *logten(18+1)

26. (1 pt) The pH scale for acidity is defined by pH = log10[H+] where [H+]is the concentration of hydrogen ionsmeasured in moles per liter (M).

A solution has a pH of 1.15.

Calculate the concentration of hydrogen ions in moles per liter

(M).

The concentration of hydrogen ions is moles per liter.Correct Answers:

0.070794578438413827. (1 pt) The fox polulation in a certain region has a relative

growth rate of 5 percent per year. It is estimated that the popu-

lation in the year 2000 was 14700.

(a) Find a function that models the population t years after

2000 (t= 0 for 2000).Your answer is P(t) =

(b) Use the function from part (a) to estimate the fox popu-

lation in the year 2008.

Your answer is (the answer must be an integer)

Correct Answers:

14700*exp(0.05*t)

2192928. (1 pt) The 1985 Mexico City eqrthquake had a magnitude

of 8.1 on the Richter scale. The 1976 earthquake in Tangshan,

China, was 1.26 times as intense. What was the magnitude of

the Tangshan eqrthquake?

Your answer is .

Correct Answers:

5


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8.20037054511756

29. (1 pt) Match the functons with their graphs. Enter the let-

ter of the graph below which corresponds to the function. (Click

on image for a larger view )

1. y = 1cosx2. y = 1 + sinx3. y = 42cosx4. y =2sinx

A B C D

Correct Answers:

B D

C

A



(Click on image for a larger view )

1. y = cos(x/80)2. y = esin20x

3. y = cos(100x)4. y = sin(x/40)

A B C D

Correct Answers:

D B C A

31. (1 pt)

Let y =15cos[5(x + 5

)].What is the amplitude?

What is the period?

What is the phase shift?

[NOTE: If needed, you can enter as pi in your answers.]Correct Answers:

15 1.25663706143592 -0.628318530717959

32. (1 pt)

Enter T or F depending on whether the statement is true or

false (You must enter T or F True and False will not work.)

1. y = tan(2x) has period 2. sec(x) and tan(x) are undefined for the same values of

x3. sin(x) is odd and cos(x) is even4. The domain of tan(x) is all real numbers

Correct Answers:

F T T F

33. (1 pt) Fill in the blanks:

1. If tanx =1 then tan(x) =2. If sinx = 0.8 then sin(x) =3. If cosx = 0.1 then cos(x)=4. If tanx = 3 then tan(+x)=Correct Answers:

1 -0.8 0.1 3

34. (1 pt) For y =10cos(x 7

),its amplitude is ;

its period is ;

its phase shift is ;

Correct Answers:

10 6.28318530717959 0.448798950512828

35. (1 pt) Evaluate the following expressions. Your answer

must be an angle/2 in radians, written as a multipleof. Note that is already provided in the answer so you sim-

ply have to fill in the appropriate multiple. E.g. if the answer is

/2 you should enter 1/2. Do not use decimal answers. Writethe answer as a fraction or integer.

sin1(sin((7/4)) =

sin1

(sin(7

/6))=

cos1(cos(5/4))= cos1(cos(/6))=

Correct Answers:

0.25 -0.166666666666667 0.75 0.166666666666667

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36. (1 pt) Evaluate the following expressions. Your answer

must be an angle in radians and in the interval [/2,/2]. Notethat is already provided in the answer so you just have to write

the appropriate multiple. E.g. if the answer is /2 you shouldwrite 1/2. Do not use decimal numbers. The answer should be

a fraction or an integer.

(a) tan1(tan(3/4)) = (b) tan1(tan(2/3)) = (c) tan1(tan(5/6)) = Correct Answers:

-0.25 -0.333333333333333 0.166666666666667

37. (1 pt) Find the value of each expression if defined; oth-

erwise, input undefined.

(a) tan(tan1 6) = .(b) sin1[sin(

6)] = radians.

Correct Answers:

6 -0.523598775598299

Generated by the WeBWorK system cWeBWorK Team, Department of Mathematics, University of Rochester

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20121 calc dei adrian.jarriagam.tarea3p1respuestas

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