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MATH 107, QUIZ 5 Extended due date: Wednesday, October 6, 2021

NAME: _______________________________

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I have completed this assignment myself, working independently and not consulting anyone except the instructor.

INSTRUCTIONS

· There are 7 problems (on 6 pages), some with multiple parts. The quiz is worth 100 points, equivalent to 9% of your final course grade. This quiz is open book and open notes . This means that you may refer to your e-text/textbook, notes, and online classroom materials, but you must work independently and may not consult anyone (and confirm this with your submission). You may take as much time as you wish, provided you turn in your quiz no later than 11:59 PM (US Eastern Time Zone) Wednesday, October 6, 2021, the extended due date.

· Show work/explanation. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is acceptable also; a single file in pdf format, with your name and quiz number in the file name, is preferred. In your document, be sure to include your name and the assertion of independence of work.

· If you have any question, please post it in “Ask the Professor” discussion on LEO if the answer to your question would benefit others in class; otherwise, please contact me privately via e-mail.

PLEASE READ THE QUESTIONS/PROBLEMS CAREFULLY; SHOW ALL YOUR WORK AND REASONING, Just the answer, without supporting work, will receive no credit.

1. (5 points) Solve the following equation:

2

2. [26 points] The surface area s of a highly expandable, advertisement beach ball (a sphere) is a function of its diameter d and is given by the formula s(d) = π d2, where π 3.14. Suppose that the last season’s beach ball, with some filling gas remaining in it, is to be inflated for the new season and its diameter increases with time due to inflation according to the formula d(t) = t2 + 10, where t is measured in seconds, t ≥ 0, and d is measured in inches.

Showing your work, answer the following questions (round final answers to two decimal places and provide units):

(a) What is the diameter of the beach ball before inflation begins for the new season? (Do not forget the unit.)

(b) What is the surface area of the beach ball before inflation begins for the new season? (Do not forget the unit.)

(c) What is the diameter of the beach ball for an inflation time of nine seconds? (Do not forget the unit.)

(d) What is the surface area of the beach ball for an inflation time of nine seconds? (Do not forget the unit.)

(e) Find and interpret (s ○ d)(t).

(f) Using your answer to Part (e), and showing your work, find (s ○ d)(0) as a factor of π first, and then in decimal format with unit.

(g) Using your answer to Part (e), and showing your work, find (s ○ d)(9) as a factor of π first, and then in decimal format with unit.

(h) Supporting your answer briefly, show the mathematical domain of the function (s ○ d)(t) in interval notations.

(i) Showing your work, determine the physical/applied (real life) domain of the function (s ○ d)(t) within the context of the problem, knowing that, according to the manufacturer, the beach ball will explode when its diameter exceeds 85 inches?

3. [10 points]

(a) Write the function h(x) = 5 x2 as a composition of non-identity functions q(x) and r(x). In other words, find r(x) and q(x) such that (r○q)(x) would result in the h(x), not choosing any identity function.

(b) Check your answer by composing your q(x) with r(x).

4. [11 points]

(a) How, based on the graph of a function, we can tell that the function has an inverse?

(b) Apply your prescription to the following graphs and state which one, if any, is invertible.

(c) In case an invertible function is noted, draw the graph of its inverse.

5. [20 points]

(a) Without resorting to graphing, and before applying the inverse-finding steps, how can we determine whether the function given below has an inverse? Show your work.

(b) Find the inverse function (x).

(c) Check your answer to Part (b). To check your answer to Part (b), it is required to show:

(○ and (

(d) Write the domain and the range of g(x) in interval notations.

(e) Write the domain and the range of in interval notations.

6. [10 points] Find exact solution(s) for the following equations:

7. [18 points]

(a) Suppose that you are given the graph of a base b exponential function, drawn on the x-y plane. Briefly explain how the value of base b can be found from the graph.

(b) Solve the equation

(c) Given the equation ln(10x) = 10, find x.

(d) A calculator cannot directly find log13 (471) but has the built-in functions for base-10 logarithm and/or the natural logarithm. Showing your work, compute the value of log13 (471) using the capability of that calculator.

(e) Using the figures and Theorem on page 423 of the e-book, set up a sign chart for the log function with a base greater than 1 and a sign chart for the log function with a base between 0 and 1, each reflecting the signs, the zero of the function, and the asymptote.

(f) For a value of x > 1, do we have log(x) = ln(x), log(x) < ln(x), or log(x) > ln(x)? Support your answer briefly, without using any numerical value for x.

End of quiz: please do not forget to write and sign (or type) the required statement reflected after “NAME:” at the top of page 1 of the quiz in case what you post does not contain the said page reflecting your signature and date.

1

1

MATH 107

, QUIZ

5

Extended due date:

Wednesday

,

October 6

, 2021

NAME:

_______________________________

I have completed this assignment myself, working independently and not consulting anyone except the

instructor.

INSTRUCTIONS

·

There are

7

problems

(

on

6

pages

),

some

with

multiple parts.

The quiz is worth 100 points

, equivalent to

9

%

of

your final course grade. This quiz is

open book

and

open

notes

. This means that you may refer to your

e

text/

textbook, notes, and online classroom materials, but

you must work independently and may not consult

anyone

(and confirm this with your submission). You may take as much time as you wish, provided you tur

n in

your quiz no later than

11:59 PM (US Eastern Time Zone)

Wednesday

,

October 6

,

20

2

1

, th

e extended due date

.

·

Show work/explanation. Answers without any work may earn little, if any, credit.

You may type or write your

work in your copy of the quiz, or if you prefer, create a docume

nt containing your work. Scanned work is

acceptable also;

a single file in pdf format, with your name and quiz number in the file name,

is preferred.

In

your document,

be sure to include your name and the assertion of independence of work.

·

If you have an

y question, please post it in “Ask the Professor” discussion on LEO if the answer to your question

would benefit others in class; otherwise, please contact me privately via e

mail.

PLEASE READ THE QUESTIONS/PROBLEMS CAREFULLY;

SHOW ALL YOUR WORK AND REASO

NING,

Just the answer,

without supporting work, will receive no credit.

1.

(

5

points)

Solve the following equation:

2

?

??

+

2

=

2

2.

[

2

6

points

]

The surface area

s

of a

hig

h

ly expandable

,

advertisement

beach

ball

(a sphere)

is a

function of its

diameter d

and is given by the formula

s(

d

) = π

d

2

,

where

π

»

3.14

.

Suppose that

the

last season’s

beach

ball

,

with some filling gas remaining in it,

is to be inflated for the new season and

its

diameter

increases with time

due to inflation

according to the formula

d

(t) =

??

??

t

2

+

1

0

, where

t

is

measured in seconds,

t

=

0

, and

d

is measured in inches.

Showing your work, answer the following questions

(round final answers to

two decimal places

and

provide units):

(a)

What is the

diameter

of the

beach

ball

before inflation begins for the new season? (Do not forget

the unit.)

1

MATH 107, QUIZ 5 Extended due date: Wednesday, October 6, 2021

NAME: _______________________________

I have completed this assignment myself, working independently and not consulting anyone except the

instructor.

INSTRUCTIONS

 There are 7 problems (on 6 pages), some with multiple parts. The quiz is worth 100 points, equivalent to 9% of

your final course grade. This quiz is open book and open notes. This means that you may refer to your e-

text/textbook, notes, and online classroom materials, but you must work independently and may not consult

anyone (and confirm this with your submission). You may take as much time as you wish, provided you turn in

your quiz no later than 11:59 PM (US Eastern Time Zone) Wednesday, October 6, 2021, the extended due date.

 Show work/explanation. Answers without any work may earn little, if any, credit. You may type or write your

work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is

acceptable also; a single file in pdf format, with your name and quiz number in the file name, is preferred. In

your document, be sure to include your name and the assertion of independence of work.

 If you have any question, please post it in “Ask the Professor” discussion on LEO if the answer to your question

would benefit others in class; otherwise, please contact me privately via e-mail.

PLEASE READ THE QUESTIONS/PROBLEMS CAREFULLY; SHOW ALL YOUR WORK AND REASONING, Just the answer,

without supporting work, will receive no credit.

1. (5 points) Solve the following equation:

-2 – ??+2=2

2. [26 points] The surface area s of a highly expandable, advertisement beach ball (a sphere) is a

function of its diameter d and is given by the formula s(d) = π d

2

, where π  3.14. Suppose that the

last season’s beach ball, with some filling gas remaining in it, is to be inflated for the new season and

its diameter increases with time due to inflation according to the formula d(t) =

??

??

t

2

+ 10, where t is

measured in seconds, t = 0, and d is measured in inches.

Showing your work, answer the following questions (round final answers to two decimal places and

provide units):

(a) What is the diameter of the beach ball before inflation begins for the new season? (Do not forget

the unit.)

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