Question

MATH125: Unit 1 Individual Project Answer Form

Mathematical Modeling and Problem Solving

ALL questions below regarding SENDING A PACKAGE and PAINTING A
BEDROOM must be answered. Show ALL step-by-step calculations, round
all of your final answers correctly, and include the units of
measurement. Submit this modified Answer Form in the Unit 1 IP
Submissions area.

All commonly used formulas for geometric objects are really
mathematical models of the characteristics of physical objects. For
example, a basketball, because it is a sphere, can be partially
modeled by its distance from one side through the center (radius,
r) and then to the other side by the diameter formula for a sphere:
D = 2r.

For familiar two-dimensional variables length, L, and width, W, the
perimeter and area formulas for a rectangle are mathematical models
for distance around the rectangle (perimeter, P) and the region
enclosed by the sides (area, A), respectively:

P = 2L + 2W and A = L x W

Along with another variable, height, H, a three-dimensional
rectangular prism’s volume and surface area can be measured. For
example, the formulas for a common closed cardboard box’s inside
space (volume, V) and outside covering (surface area, SA) are
respectively:

V = L x W x H and SA = 2(L x W) + 2(W x H) + 2(L x H)

For this IP assignment follow Polya’s principles to solve your
chosen problem, and include the following:

Explain your interpretation of what the problem is about.

Develop and write down a strategy for solving this problem; show
the steps in the correct order for your attempted solution.

Did your strategy actually solve the problem? How do you
know?

Suppose your solution did not solve the problem—what would be your
next action?

SENDING A PACKAGE

Your goal is to construct a rectangular box with a top on it that
has the smallest possible surface area in which a football and a
basketball, both fully inflated, will just fit into at the same
time. The following are the measurements of the football and
Mathematical

What box dimensions make a good model for this situation? All
quantities are inside-of-the-box measurements. First, position the
football and basketball side-by-side. Then, slide the basketball so
that it is even with one point of the football. Now, measurements
can be made that will give the minimum width across both objects.
That will be the minimum width of the box with the smallest surface
area. Using the following diagrams, first find the exact LENGTH and
HEIGHT:

ANSWERS

LENGTH 11.55 inches

HEIGHT 9.55 inches

6

Explain your answer here:

Football is the longest item I got the from the football which
11.55”

And the has the height which is 9.55”

Note that the diameters combined include an overlap; see the
cross-section perspective below. To find the WIDTH, you must first
account for this by applying the Pythagorean theorem. The WIDTH
will be the radius of the football plus the side b of the right
triangle below plus the radius of the basketball.

Here is the right triangle shown larger and labeled:

Find a and c. The measure of the hypotenuse, c, is the sum of the
two balls’ radii. The smaller side, a, is the difference of these
two radii. Find these two exact sides including the units of
measurement:

ANSWERS

a
2.0”

c 42.2”

Explain your answer here: a = 11.55 – 9.55
= 2.0 the difference of the two radii.

c = 11.55(2) + 9.55(2) = 84.40 the units of measure

Next, find b. Apply the Pythagorean theorem,a^2+b^2=c^2, using its
form:

b=√(c^2-a^2 )

Show all step-by-step calculations, including the units of
measurement, and round your final answer to the nearest
hundredth:

ANSWER

b 4.48

Explain your answer here:

C = 11.55(2) + 9.55(2) = 42.20(2)

b = the square root of C to the second power minus a to the second
power

Now, list all of the box’s dimensions in the chart below. Recall
from above: The WIDTH will be the radius of the football plus the
radius of the basketball plus the side b of the right triangle
above.

Show all step-by-step calculations, including the units of
measurement, and round your final answers to the nearest
tenth:

ANSWERS

LENGTH

WIDTH

HEIGHT

Explain your answer here:

Using Polya’s technique for solving problems, describe and discuss
the strategy, steps, formulas, and procedures you will use to solve
this problem.

Explain your answer here:

The minimum surface area corresponds to the minimum volume. Using
the formula and dimensions from above, find the box’s volume.

Show all step-by-step calculations, including the units of
measurement, and round your final answers to the nearest whole
measurement unit:

ANSWER

Volume

Explain your answer here:

Using the formula and dimensions from above, find the box’s surface
area.

Show all step-by-step calculations, including the units of
measurement, and round your final answers to the nearest whole
measurement unit:

ANSWER

Surface Area

Explain your answer here:

Demonstrate that your solution is correct. In other words, explain
why the box you have created is the smallest possible box.

Explain your answer here:

Answer #1

P = 2L + 2W and A = L* W
V = L * W * H and SA = 2(L * W) + 2(W * H) + 2 (L * H)
sending a package
your goal is to construct a rectangle box with a top on it that
has a smaller possible surface area in which a football and a
basketball , both fully inflated, will just fit into at the same
time.The football measures 6.5 inches high and...

NAME:
MATH125: Unit 3 Individual Project Answer Form
Logic, Decision Making, and Introduction to Statistics
ALL questions below regarding BUYING and LEASING a car must be
answered. Show ALL step-by-step calculations, round all of your
final price answers correctly to the nearest cent, and include the
units of measurement. Submit this modified Answer Form in the Unit
3 IP Submissions area.
Being well-informed, or at least knowing the right questions to
ask, can save you from being taken advantage of....

For full credit be sure to show all work and units.
1. A 20 foot ladder leans against a vertical wall. The bottom of
the ladder slides away from the wall at 2 ft/sec.
a. How fast is the top of the ladder sliding down the wall when
the top of the ladder is 12 feet from the ground?
b. Interpret the meaning of the sign.
2. The current speed record for weight loss is 487 pounds to 130
pounds...

1) Answer each of the following problems. SHOW ALL NECESSARY
WORK to fully justify each of your answers.
a) From a box of 24 tiny dolls, A toddler selects a set of 6
dolls as her favorites . How many different ways can she make this
selection?
b) In how many different ways can the eleven players of a
football team line up to be in a photograph
c) A store has to hire two cashiers. Five people are interviewed...

1. Use the data that is posted below to answer the following
questions. If your answer has units to it, then please state those
units.
Production Options
Sugar beets (tons)
Wheat (tons)
A
200
0
B
180
20
C
140
40
D
80
60
E
0
80
a) Graph Production Possibilities Frontier (Curve) for Sugar
Beets and Wheat. Put sugar beets on the vertical axis and label
that axis Sugar Beets and put wheat on the horizontal axis and
label that...

answer all questions
3.13.6
Question 110 pts
A 319 kg motorcycle is parked in a parking garage. If the car has
35,494 J of potential energy, how many meters above ground is the
car? Report your answer to 1 decimal place. Please do not include
units or the answer will be marked incorrect.
Flag this Question
Question 210 pts
A box sitting on the top of a hill has 252 J of potential energy.
If the hill is 279 meters...

Answer all the questions below in paragraph form. Atleast 2
paragraphs.
CASE STUDY
In the Appliances Manufacturing Plant, a large number of
engineering activities are carried out in a wide range of areas.
These activities include design, production of parts, assembly,
testing, and quality assurance.
Many of the manufacturing processes in the plant are performed
using automated technologies and equipment. People also perform
some of the manufacturing tasks and the plant employs over 400
workers. The decision on whether people...

Answer all the questions below in paragraph form. Atleast 2
paragraphs.
Case Study
In Francisco Automotive Manufacturing Plant, a large number of
engineering activities are carried out in a wide range of areas.
These activities include design, production of parts, assembly,
testing, and quality assurance.
Many of the manufacturing processes in the plant are performed
using automated technologies and equipment. People also perform
some of the manufacturing tasks and the plant employs over 400
workers. The decision on whether people...

Please answer entire problem(its only one question)
2. Change all of the numbers in the data area of your worksheet
so that it looks like this:
A
B
C
D
1
Chapter 3: Applying Excel
2
3
Data
4
Unit sales
60,000
units
5
Selling price per unit
$10
per unit
6
Variable expenses per unit
$6
per unit
7
Fixed expenses
$228,000
8
If your formulas are correct, you should get the correct answers
to the following questions.
(a)...

do all five questions
Question 1
20 pts
Ignoring the effects of air resistance, if a ball falls freely
toward the ground, its total mechanical energy
Group of answer choices
increases
remains the same
not enough information
decreases
Flag this Question
Question 2
20 pts
A child jumps off a wall from an initial height of 16.4 m and lands
on a trampoline. Before the child springs back up into the air the
trampoline compresses 1.8 meters. The spring constant...

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