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Math Quiz 3 Math Quiz 3

Date added: 07/09/2012
Date modified: 07/09/2012
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Math Quiz 3Q1
Question 1
A bank offers to sell a bank note that will reach a maturity value of $12,000 in 12 years. How much should you pay for it now if you wish to receive an 8% return on your investment?

1)    $925.93
2)    $4594.71
3)    $11,040.00
4)    $920.00

Question 2
In 1995 an investor put $2000 in an account which paid 8%. In 2005 she withdrew $1000 from the account. What will the account be worth in 2020 ?

1)    $13,778.11
2)    $11,458.00
3)    $7389.06
4)    $3451.08

Question 3
The Polymerase Chain Reaction (PCR) is used to replicate segments of DNA. It is used to make DNA samples big enough for testing, starting from very small samples collected, for instance, from a crime scene. PCR can double the number of a particular DNA segment every two minutes. If one wants a DNA sample with   copies of a particular segment, how long must the PCR process be carried out to produce them? Assume that there is just one segment in the original sample.

1)    106 minutes
2)    53 minutes
3)    18 minutes
4)      minutes

Question 4        4 / 4 points
An electrical power supply, such as a battery, generates an electrical potential (voltage, V) which varies depending on how much current (i) it is delivering. The integral   represents the total power (energy per unit time) being given off by the battery when it is producing a current I. The useful electricalpower, however, is just the product  . The difference between the total and the electrical power represents power that is wasted (and that accumulates as heat). Consider a hypothetical battery with a voltage vs. current curve described by the equation  .   If the battery is producing a current of 4 amperes, how much electrical power is being produced, and how much power is being wasted?

Question 5        4 / 4 points
Evaluate the integral by computing the limit of Riemann sums.

Question 6        4 / 4 points
The population of New Zealand grew exponentially through the 20th century at a rate of 1.6%   . If the population in 2000 was 3.9 million, when was the population 1.0 million?

1)    1915
2)    1920
3)    1925
4)    1930

Question 7        4 / 4 points
Find the solution of the differential equation,  , satisfying the initial condition,  .

Question 8        4 / 4 points
Ba has a half-life of 2.5 hours. How long would it take for 35 mg of  Ba in a sample to decay to 1.0 mg?

1)    87.5 hours
2)    8.9 hours
3)    3.6 hours
4)    12.8 hours

Question 9        4 / 4 points
Bubba, a farmer, wants to build a pen using the 20 ft   40 ft corner of his barn as part of the pen as shown in the figure below (the corner will not require any fencing). If Bubba has 128 ft of available fencing, then what will be the maximum area?

1)    2209 square feet
2)    1764 square feet
3)    1369 square feet
4)    1024 square feet

Question 10        4 / 4 points
Determine whether or not the integral is improper.

1)    The integral is improper.  

2)    The integral is not improper.

Question 11        4 / 4 points
Find the solution to the following separable differential equation.

Question 12        4 / 4 points
Find the solution of the differential equation,  , satisfying the initial condition,  .

Question 13        4 / 4 points
$50,000 that was invested in 1990 was worth $134,100 in 2000. What annual interest rate did the investment earn in that 10 year period? Assume continuous compounding.

1)    118.06%
2)    10.91%
3)    108.20%
4)    9.87%

Question 14        4 / 4 points
Find all discontinuities.

1)    discontinuous at  

2)    discontinuous at  

3)    discontinuous at  

4)    continuous for all x

Question 15        4 / 4 points
In an AC circuit, the current has the form  for constants   The power is defined as   for a constant  . Find the average value of the power by integrating over the interval  

Question 16        4 / 4 points
Is the following differential equation separable or not?

1)    separable
2)    not separable

Question 17        4 / 4 points
Find the derivative   implicitly.

Question 18        4 / 4 points
Compute the sum of the form

for the given function and  -values, with  equal to the difference in adjacent  's.

Question 19        4 / 4 points
An object propelled from the ground with an initial velocity of 50 ft/s will reach a maximum height of 39.1 ft. If the initial velocity is increased 18%, by what percentage will the maximum height increase? Round percentages to the nearest integer.

1)    18%
2)    39%
3)    3%
4)    28%

Question 20        4 / 4 points
Using the critical numbers of  , use the Second Derivative Test to determine all local extrema.
critical numbers:  ; local max  ; local min  

2)    critical numbers:  ; local max  ; local min  

3)    critical numbers:  ; local max  ; local min  

4)    critical numbers:  ; local max  ; local min  

Question 21        4 / 4 points
Determine whether the integral converges or diverges. Find the value of the integral if it converges.

1)    converges to 0
2)    converges to  

3)    converges to  

4)    diverges

Question 22        4 / 4 points
Is the following differential equation separable or not?

1)    separable
2)    not separable

Question 23        4 / 4 points
Evaluate the integral using integration by parts and substitution (as we recommended in the text, "Try something!").

Question 24        4 / 4 points
Find the derivative of 

Question 25        4 / 4 points
Find the limit or explain why it does not exist.

Maths quiz 2 Maths quiz 2

Date added: 07/08/2012
Date modified: 07/08/2012
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Maths Quiz 1 Maths Quiz 1

Date added: 07/08/2012
Date modified: 07/08/2012
Filesize: 507 kB
Downloads: 4
Price 1.00 USD

Question 1
A child's height h (in inches) closely resembles a linear function in terms of the child's age a (in years) if the child is between the ages of 5 and 10. The height of a certain youngster is 46 inches when the child is age 5, and 55 inches at age 7. Find a linear function relating a child's height h to his or her age a.

Question 2
An observer, standing on level ground, 115 feet from the bottom of a tower, looks at the top of the tower and notices that his angle of elevation is 0.5 radians. Estimate the height, h, of the tower, rounding your answer to the nearest tenth.

A)    h = 62.8 feet
B)    h = 75.3 feet
C)    h = 81.1 feet
D)    h = 86.9 feet

Question 3Rewrite as a single logarithm and simplify, if possible.

Question 4
Determine the limit.   
Answer with a number,  ,   or that the limit does not exist.

Question 5
Suppose the length of an animal t days after birth is given by h(t).
What is the length of the animal at birth?

Question 6
Determine all vertical and slant asymptotes.
A)    vertical asymptotes:     slant asymptote: 

B)    vertical asymptote:   slant asymptote: 

C)    vertical asymptote:   slant asymptote: 

D)    vertical asymptotes:     slant asymptote: 

Question 7
Find the equation of the tangent line to   at 

Question 8
Find the derivative of  .

Question 9
A bacterial population starts at 300 and quadruples every day. Calculate the percent rate of change rounded to 2 decimal places.
A)    160.94 %
B)    138.63 %
C)    1.39 %
D)    88.63 %

Question 10
Suppose a snowball melts in such a way that it maintains a spherical shape. If the radius is decreasing at a rate of 1.75 cm per hour when the radius is 6 cm, how fast is the volume of the snowball decreasing at that instant?
A)    791.7 cm3/hr
B)    263.9 cm3/hr
C)    583.2 cm3/hr
D)    1045.0 cm3/hr

Question 11
The total cost of producing and marketing x number of units of a certain product is given by  . For what number x is the total cost a minimum? Round answer to nearest unit.

Question 12
Given the graph of  , locate the absolute extrema (if they exist) on the interval  .
A)    absolute max: 

B)    absolute min: 

C)    absolute min: 

D)    no absolute extrema

Question 13
Find an antiderivative by reversing the chain rule, product rule or quotient rule.

Question 14
Find the position function   from the given velocity function and initial value. Assume that units are feet and seconds.

Question 15
Evaluate the integral.

Question 16
Evaluate the derivative using properties of logarithms where needed.

Question 17
Identify the graph and the area bounded by the curves   on the interval  .

Question 18
When pumping water out of a full hemispherical basin with radius r feet, how far down will the water level be when 1/5 of the work has been done? [The density of water is 62.4 lbs/ft3.]

Question 19
Find the volume of the solid with cross-sectional area   extending over the range  .

Question 20
Use cylindrical shells to compute the volume of the solid formed by revolving the region bounded by   abouty = 10.

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