math project - weebly · 2019. 8. 3. · task1& • done&by&ohoud&khamis&alkaabi&& •...
TRANSCRIPT
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MATH PROJECT GRADE 12.55
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OBJECTIVE • In the STEM Research Project Challenge,
teams will learn more about the fields of Science, Technology, Engineering, and Mathema@cs (STEM) and how they are
related to sequences and series. • Teams will use this Project Challenge to
explore how Arithme@c sequences and series can apply to science, technology,
and engineering.
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TASK 1
• DONE BY Ohoud Khamis AlKaabi • Task 1 is About The Bouncing Ball • Level (Science – Physics)
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Short video
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• On each bounce, Ball 1 reaches a height equal to 3/4 of the height of its previous bounce. On the first bounce, it achieves a height of 25 feet. Ball 2, which reaches a height of 18 feet on its first bounce, bounces 4/5 of the height of its previous bounce on each bounce.
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1. Filling the table, showing the height of each ball for each bounce.
Bounce Ball 1 height feet Ball 2 height feet
1
2
3
4
5
6
7
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• 2. Will Ball 2 ever bounce higher than Ball 1? If so, at which bounce? • 3. For how many bounces do both balls bounce above 10 feet? • 4. When do the balls “stop” bouncing (i.e., achieve a height of less than 3
inches)?
• 5. What minimum ini`al bounce height (to the nearest foot) would you have to ensure for each ball in order to guarantee that it bounces at least 8 feet high by the sixth bounce?
• 6. Calculate the sum of all of the bounce heights for both balls.
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Task 2
• DONE BY Maitha Saif AlKaabi • Task 2 is About Don’t Break the Chain • Level (Technology)
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These chain emails rely on each person that receives the email to forward it on. Have you ever wondered how many people might receive the email if the chain remains unbroken? To figure this out, assume that it takes a day for the email to be opened, forwarded, and then received by the next person. On day 1, Bill Weights starts by sending the email out to his 8 closest friends. They each forward it to 10 people so that on day 2, it is received by 80 people. The chain con`nues unbroken.
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Ques@ons 1 to 3: • 1. How many people will receive the email on day 7?
• 2. How many people with receive the email on day n? Explain your answer with as many representa@ons as possible.
• 3. If Bill gives away a Super Bowl that costs $4.95 to every person that receives the email during the first week, how much will he have spent?
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Task 3
• DONE BY Zahra Ali AlBlooshi • Task 3 is About Arithme`c Sequence • Level (Engineering)
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Short video
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• Consider a pillar drill that has 6 different sized pulleys. These pulleys operate from a motor running at a constant speed. The largest pulley rotates at 30 rpm and the smallest at 200rpm. Given that the speeds are arranged according to an arithme`c sequence calculate the Following:
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Ques`on • 1) The Speed of the four remaining pulleys.
• 2) If the Largest Pulley rotates at 100 rpm What happens to the speeds of the other Pulleys?
• 3) If a piece of metal needs a 3000rpm drill, How can some one modify the given drill so it can have this speed of drilling?
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Task 4
• DONE BY Huda Mohammed AlEsaee • Task 4 is About Hot Air Balloon • Level (Mathema`cs)
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Short video
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• Objec@ves • Students will use an infinite geometric series to find al`tudes of a hot air
balloon. • Students will determine what makes the applica`on problem an Infinite
geometric series. • Students will use a formula and sigma nota`on to find par`al sums • (Al`tude of the hot air balloon at a given minute). • Students will use a formula and sigma nota`on to find the maximum • al`tude of the hot air balloon.
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Hot Air Balloon • Suppose you are an environmental scien`st and have
been asked to check the air quality in Abu Dhabi. To do this, you have ajached a probe to collect data to a hot air balloon that will travel over different parts of the city. As a hot air balloon rises, the air inside the balloon cools and causes the balloon to rise more slowly with each minute. Assuming air resistance is negligible, suppose the balloon rose 114 feet the first minute. For each minute aker the first minute, the hot air balloon rises 70% as far as it rose the previous minute. You will need to know the height when analyzing the data taken by the probe.
• What will be the balloon’s maximum al`tude?
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Calculate the distance the balloon travels for the first five minutes of the balloon’s flight
Minute
Distance traveled per minute
Total height
0
1
2
3
4
5
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• 1) What makes this problem a geometric sequence? Explain.
• 2) What makes this problem an infinite geometric series? What would be the value of the ra`o r?
• 3) How can you tell if this infinite geometric series has a finite sum? Explain
• 4) Use the sum of a geometric series formula given below, which will allow you to find par`al sums. In this case, you can find the al`tude of the balloon for any given minute. Find the height at 5, 6, and 10 minutes.
• 5) How would you find the same al`tudes as in Ques`on 5 using sigma nota`on?
• 6) Using the sum of an infinite geometric series formula find the maximum height of the balloon.
• 7) How would you find the maximum al`tude of the balloon using sigma nota`on
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