MATH151 Bethany Lutheran College Calculus Problem Set

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yvoen1023

Mathematics

math151

Bethany Lutheran College

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I am stuck in both of these questions. I want help with all the steps and a definition on every step. thanks.

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2) Gasoline stations store the fuel in an underground tank. Often these are shaped as right circular cylinders lying horizontally. A truck transports gasoline from North Dakota to North Mankato and fills an underground tank at Kwik Trip on highway 169. The tank is 25 feet in length and 10 feet in diameter. The gasoline flows through the delivery hose at 22.5 gallons per minute. At what rate is the height of the gasoline in the tank changing when the level of liquid in the tank is 9 feet deep? Vent Pipes Fill Pige Delivery Hose 4) i) Suppose that you purchased $100 worth of stock in Verizon on December 31, 2013. The following table indicates the value of the stock for each December 31st of the following years (any dividends have been reinvested): 2013 2014 2015 Verizon stock value 2016 $124.40 2017 $129.50 2018 $143.90 $100 $99.40 $103.00 Note that this allows January 1st to be considered day one. a) Determine a fifth degree polynomial that is the best fit for the data. Round all coefficients to the nearest ten-thousandth and let 12/31/2013 correspond to t = 0. b) Verizon is trying to analyze the behavior of the company compared to the actions of the stock to see if any correlations or causations may be developed. Therefore, determine the corresponding day for each maximum and minimum value of the polynomial. c) When is the polynomial concave up? Concave down? What information is this providing to Verizon? d) On what day is the investment growing the most rapidly? ii) Perform a similar analysis for the stock prices of a company of your choosing. Research the price of the stock on December 31 for 5 years in recent history. Cite your source. e) Create a 3rd degree polynomial that accurately reflects the data. If your coefficient of determination is less than 0.90, select a different company. f) Determine the corresponding day for each maximum and minimum value of the polynomial. g) When is the polynomial concave up? Concave down? What information is this providing to your company? h) On what day is the investment growing the most rapidly?
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Running head: CALCULUS PROBLEM SET

Calculus Problem Set
Firstname Lastname
Name of Institution

1

CALCULUS PROBLEM SET

2

Question 2
𝑆𝑜𝑙𝑢𝑡𝑖𝑜𝑛
𝑇𝑎𝑘𝑖𝑛𝑔
𝑉, 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟
ℎ, ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟
𝑟, 𝑏𝑒 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟
𝑇ℎ𝑒 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 𝑖𝑠 𝑔𝑖𝑣𝑒𝑛 𝑏𝑦 𝑉 = 𝜋𝑟 2 ℎ
𝑤𝑒 𝑐𝑎𝑛 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑡𝑒 𝑡ℎ𝑒 𝑔𝑖𝑣𝑒𝑛 𝑒𝑥𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛 𝑤𝑖𝑡ℎ 𝑟𝑒𝑠𝑝𝑒𝑐𝑡 𝑡𝑜 't'

𝑤𝑒 𝑔𝑒𝑡

𝑑𝑉
𝑑ℎ
= 𝜋𝑟 2
… … … … … … … … … . (𝑖)
𝑑𝑡
𝑑𝑡

𝑑𝑉
22.5
= 22.5 𝑔𝑎𝑙𝑙𝑜𝑛𝑠 𝑝𝑒𝑟 𝑚𝑖𝑛𝑢𝑡𝑒 =
𝑓𝑡 3 𝑝𝑒𝑟 𝑚𝑖𝑛𝑢𝑡𝑒 = 3.0078 𝑓𝑡 3 ⁄𝑚𝑖𝑛𝑢𝑡𝑒
𝑑𝑡
7.48052
𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 =

10𝑓𝑡
= 5 𝑓𝑒𝑒𝑡
2

𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔 𝑡ℎ𝑒 𝑓𝑖𝑟𝑠𝑡 𝑒𝑞𝑢𝑎𝑡𝑖...


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