aths
DESCRIPTION
ATHS. Calculus Project Grade: 12 – ES. GOALS. Students will interpret their understanding of applications of integration Students will use technology for research and communication: wiki/blog. Students will present their findings to the class through digital Media(Video/Booklet). - PowerPoint PPT PresentationTRANSCRIPT
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ATHS Calculus Project Grade: 12 – ES
Done by : Grade 12-01 , ID:
Ali Al-Ali 1001299
Majid Al Yammahi 1001330
Mohammed Saeed 1001293
Ahmem Al Naqbi 1001391
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GOALS
Students will interpret their understanding of applications of integration
Students will use technology for research and communication: wiki/blog.
Students will present their findings to the class through digital Media(Video/Booklet).
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Theme /INTRO
This project covers the application of topics in calculus; students will apply the concepts and theorems they have learned on integration. Moreover students will be able to apply their knowledge in relation to vari
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TASK 1
The boundaries of a piece of land that belongs to your family can be best described as in the following graph:
i.e. the area between the −axis and 𝑥the graph of the function 𝑓( )= 3 − 5 2 +6 +5𝑥 𝑥 𝑥 𝑥
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Answer the following questions:
1. Using approximating rectangles dividing the interval from 0 to 4 into 5 equal subdivisions, estimate the area between f( )= 3 − 5 2 +6 +5 and the −axis, with ∆𝑥 𝑥 𝑥 𝑥 𝑥 x=0.8 .
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2. Calculate the exact value of the same area using the definite integral.
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Task 2 ”Oil Consumption”
Suppose that the rate of consumption of a natural resource is ′( ), where: ′( ) = .𝑐 𝑡 𝑐 𝑡 𝑘𝑒𝑟𝑡
Here is time in years, is a constant, and is 𝑡 𝑟 𝑘the consumption in the year when = 0. In 2006, 𝑡an oil company sold 1.2 billion barrels of oil. Assume that =0.04.𝑟
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b) Set up a definite integral for the amount of oil that the company will sell in the next 10 years.
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c) Evaluate the definite integral of part b.
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d) The company has about 20 billions barrels of oil in reserve. To find the number of years that this amount will last, solve the equation:
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e) Rework part d, assuming that = 0.02 𝑟
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Task 3
The annual revenue for your company over the past five years was found to follow the following Integral formula:
Where n is the number of years
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1. Verify the following relation between two consecutive years' revenue:
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2. Find the revenue of year 2, i.e. Find U2
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Task 4
A water well of depth 50 feet is used to supply people with water. A rope of weight 0.2 lbs/ft is used take the water out of the well using a barrel that weight 80 lbs when it is full of water.
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a) Calculate the work needed to lift the barrel from the bottom to the midpoint of the well.
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b) Calculate the work needed to lift the barrel from the midpoint of the well to the top of the well.
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