Southern New Hampshire University - 7-3 Project Two_ Pastry Chef Calculus
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Southern New Hampshire University *
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140
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
10
Uploaded by brienncaervin
2/24/24, 10:44 PM
Southern New Hampshire University - 7-3 Project Two: Pastry Chef Calculus
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MAT-140-X3745 Precalculus 24EW3 : MAT-140 : 1466672
,
Brie Ervin, 2/23/24 at 11:21:20 PM EST
Question1:
Score 0/1
Emily has been hired to create a cake with a diameter of feet for a special event.
However, the client has requested that one of the cake layers be cut into a specific shape to match the theme of the event.
The client has requested that Emily cut the layer into a sector of a circle with an angle of radians. Emily needs to
calculate the area of the sector to determine how much cake batter she will need to make for that layer.
Round your answer to four decimal places.
Your response
Correct response
605.5136
605.2802±1E-4
Auto graded
Grade:
0/1.0 ft
Show your work and explain, in your own words, how you arrived at your answer.
Answers with no relevant
explanations may receive reduced or no credit.
Ungraded
Grade:
0/1.0
Total grade: 0.0×1/2 + 0.0×1/2 = 0% + 0%
Question2:
Score 0.5/1
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Emily needs your help with building a display for cakes. She wants to include a small roof over the display to provide
some shade and protection from the elements. She is trying out different measurements to see what works best for the
display. Emily draws a right triangle showing the height and base of one side of the roof. (
Figure 1). She sends you a copy of
the diagram along with a calculation that she needs your help with. Figure 1
Enter the exact answer.
Your response
Correct response
3/11
Auto graded
Grade:
1/1.0 Show your work and explain, in your own words, how you arrived at your answer.
Answers with no relevant
explanations may receive reduced or no credit.
To find the value of tan(B), I used the definition of the tangent function in a right triangle for a right triangle:
Ungraded
Grade:
0/1.0
Total grade: 1.0×1/2 + 0.0×1/2 = 50% + 0%
Question3:
Score 0.5/1
Emily is preparing for an upcoming event where she will be using props designed by someone else. She needs to find the
exact calculations for an angle that has been given in radians so that she can ensure that the props are set up correctly.
The angle in question is radians. Emily specifically needs to know the exact value of the sine of this angle. Find the exact value of .
11
3
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Southern New Hampshire University - 7-3 Project Two: Pastry Chef Calculus
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Your response
Correct response
sqrt(2)/2
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Grade:
1/1.0 Show your work and explain, in your own words, how you arrived at your answer.
Answers with no relevant
explanations may receive reduced or no credit.
Ungraded
Grade:
0/1.0
Total grade: 1.0×1/2 + 0.0×1/2 = 50% + 0%
Question4:
Score 0.33/1
Now that you've helped Emily with her prop design, she needs your help with creating a pastry in the shape of a tilted
cone. However, the angle of inclination given to her in the recipe details is not in the standard unit circle. To determine
the correct dimensions for the pastry, Emily needs to use reference angles. This will allow her to calculate the correct
height and radius for the pastry design. The angle is . Emily needs your help using reference angles to evaluate .
Enter the exact answers.
For the number , either choose from the bar at the top or type in Pi (with a capital P).
The reference angle is Your response
Correct response
Pi/4
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Grade:
0/1.0 Your response
Correct response
Auto graded
Grade:
1/1.0 Show your work and explain, in your own words, how you arrived at your answer.
Answers with no relevant
explanations may receive reduced or no credit.
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is the equivalent angle
=
Ungraded
Grade:
0/1.0
Total grade: 0.0×1/3 + 1.0×1/3 + 0.0×1/3 = 0% + 33% + 0%
Question5:
Score 0.5/1
Emily was asked to make a cake for a math-themed birthday party. The cake was decorated with mathematical symbols,
and the guests were math enthusiasts. As part of the entertainment, the party organizer set up a math quiz for the guests. One of the questions was about
trigonometry, and Emily was asked to help grade the quiz. The question was: If , what is ?
Help Emily find the correct answer to this question.
Enter the exact answer.
Your response
Correct response
9/2
Auto graded
Grade:
1/1.0 Show your work and explain, in your own words, how you arrived at your answer.
Answers with no relevant
explanations may receive reduced or no credit.
Ungraded
Grade:
0/1.0
Total grade: 1.0×1/2 + 0.0×1/2 = 50% + 0%
Question6:
Score 0.5/1
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Emily is preparing to bake a cake for a company that sells musical instruments and she wants to incorporate a sound
wave pattern into the design. As part of her preparations, Emily decided to use the equation of a sine graph to create the sound wave pattern for the
cake design. The equation of the graph was given by the function: .
Emily knew that she needed to understand the properties of the sine graph, such as amplitude and period, to accurately
create the sound wave pattern for the cake. She also knew that the amplitude of the graph represented the maximum
height of the cake, and the period of the graph represented the distance between each crest of the sound wave. Can you help Emily determine the amplitude and period of the sine graph to create the sound wave pattern graph for two
periods for her circular cake design? For the given function, determine its amplitude and period, and then graph it for two periods.
Enter the exact answers.
For the number , either choose from the bar at the top or type in Pi (with a capital P).
Amplitude: Your response
Correct response
3
3
Auto graded
Grade:
1/1.0 Period: Your response
Correct response
2*Pi
Auto graded
Grade:
1/1.0 Using your answers for the amplitude and period, select the correct graph of the function .
Your response
Correct response
Auto graded
Grade:
0/1.0 Show your work and explain, in your own words, how you arrived at your answers.
Explain how you used your
answers for the amplitutde and period in selecting your graph. Answers with no relevant explanations may receive
reduced or no credit.
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Ungraded
Grade:
0/1.0
Total grade: 1.0×1/4 + 1.0×1/4 + 0.0×1/4 + 0.0×1/4 = 25% + 25% + 0% + 0%
Question7:
Score 0.75/1
Emily wants to create a new dessert that has a wavy pattern on the frosting. She decides to use the function to create the pattern. Help Emily to determine the amplitude, period, and midline of the
function to ensure that the pattern looks the way she intends it to.
Enter the exact answers.
For the number , either choose from the bar at the top or type in Pi (with a capital P).
Ampliude: Your response
Correct response
2
2
Auto graded
Grade:
1/1.0 Period: Your response
Correct response
2*Pi
Auto graded
Grade:
1/1.0 Midline: Your response
Correct response
6
6
Auto graded
Grade:
1/1.0 Show your work and explain, in your own words, how you arrived at your answers.
Answers with no relevant
explanations may receive reduced or no credit.
Ungraded
Grade:
0/1.0
Total grade: 1.0×1/4 + 1.0×1/4 + 1.0×1/4 + 0.0×1/4 = 25% + 25% + 25% + 0%
Question8:
Score 0.75/1
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Emily is using another wavy pattern on a large cake that she wants to be consistent. She decides to use the function to create the pattern. Help Emily to determine its stretching factor and phase shift, and then graph it for
two periods. Identify the correct pattern below. Enter the exact answers.
Stretching factor Your response
Correct response
6
6
Auto graded
Grade:
1/1.0 Phase shift: Your response
Correct response
no phase shift
no phase shift
Auto graded
Grade:
1/1.0 Using your answers for the stretching factor and phase shift, select the correct graph of the function .
Your response
Correct response
Auto graded
Grade:
1/1.0 Show your work and explain, in your own words, how you arrived at your answers.
Explain how you used your
answers for the stretching factor and phase shift in selecting your graph. Answers with no relevant explanations may
receive reduced or no credit.
Ungraded
Grade:
0/1.0
Total grade: 1.0×1/4 + 1.0×1/4 + 1.0×1/4 + 0.0×1/4 = 25% + 25% + 25% + 0%
Question9:
Score 0/1
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8/10
Emily needs to deliver her baked goods to her customers. She needs to load her truck with various baking equipment,
ingredients, and finished products. To load her truck, she decides to use a loading ramp and she needs to ensure that the
angle is not too steep for her to use.
Emily places a loading ramp next to her truck. The height of the ramp is feet, and an inclined portion of the ramp is feet long. What angle does the ramp make with the ground?
Round your answer to one decimal place.
The ramp makes an angle of Your response
Correct response
19.5
16.6±0.1
Auto graded
Grade:
0/1.0 degrees with the ground.
Show your work and explain, in your own words, how you arrived at your answer.
Answers with no relevant
explanations may receive reduced or no credit.
Ungraded
Grade:
0/1.0
Total grade: 0.0×1/2 + 0.0×1/2 = 0% + 0%
Question10:
Score 0.5/1
Emily has been commissioned to create a pastry design for a college math class that can serve the dual purpose of being
a tastry treat as well as a matching quiz for the students to test their knowledge of trigonometric identities. To assist with
the design process, Emily has received a list of mathematical expressions involving trigonometric identies from the
professor. However, as she is creating the treats, she realizes that she is missing the solution key! Since it is too late in
the day for her to reach out to the professor, Emily asks you for help with simplifying some of these identities. Use basic identities to help Emily to simplify .
Enclose arguments of functions in parentheses. For example, .
Remember that writing sin(x) to the fourth power as is just a mathematical shorthand. You should write it as , which is what Mobius expects.
Your response
Correct response
cos(x)
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Show your work and explain, in your own words, how you arrived at your answer.
Answers with no relevant
explanations may receive reduced or no credit.
is the answer you will arrive to after you simpfly Ungraded
Grade:
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Total grade: 1.0×1/2 + 0.0×1/2 = 50% + 0%
Question11:
Score 0.5/1
Emily has been asked to create a game using cupcakes for a convention. The organizers have given her an interesting
challenge: they want her to decorate cupcakes that incorporate math problems! Specifically, they would like her to
decorate cupcakes that use trigonometry formulas. Emily decides to create cupcakes that involve the trigonometric
identities where the event attendees will be challenged to match up the expression on one cupcake with the correct
rewritten answer displayed on another cupcake. One of the problems she needs to solve involves rewriting in terms of and . How would
Emily rewrite this for the matching cupcake in the game? Enclose arguments of functions in parentheses. For example, .
Your response
Correct response
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Grade:
1/1.0 Show your work and explain, in your own words, how you arrived at your answer.
Answers with no relevant
explanations may receive reduced or no credit.
, = Ungraded
Grade:
0/1.0
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Total grade: 1.0×1/2 + 0.0×1/2 = 50% + 0%
Question12:
Score 0.5/1
Emily loves experimenting with new ingredients and techniques to create delicious desserts. One day, while preparing
for a competition, she decides to use a unique gas to create a stunning effect in her pastry. She uses oxygen gas to create
a beautiful blue flame on top of her dessert. Emily remembers learning about the ideal gas law in school, which states that the volume of an ideal gas varies
directly with the temperature and inversely with the pressure . She realizes that this law can help her determine the
pressure of the oxygen gas in her cylinder under different conditions. Currently, the oxygen gas in her cylinder is at a temperature of degrees K and a pressure of atmospheres in a
volume of liters. Emily wants to decrease the volume to liters and increase the temperature to degrees K, but
she needs to know the new pressure to make sure the gas will still work for her dessert display.
Round your answer to two decimal places.
The pressure is
Your response
Correct response
23.47
23.47±0.01
Auto graded
Grade:
1/1.0 atmospheres.
Show your work and explain, in your own words, how you arrived at your answer.
Answers with no relevant
explanations may receive reduced or no credit.
Ungraded
Grade:
0/1.0
Total grade: 1.0×1/2 + 0.0×1/2 = 50% + 0%