An oil spill is modelled as a circular disc with radius r km and area A km

Question:

An oil spill is modelled as a circular disc with radius r km and area A km². The rate of increase of the area of the oil spill, in km2/day at time t days after it occurs is modelled as:

a. Show that

Given that the radius of the spill at time t = 0 is 1 km, and the radius of the spill at time t = π² is 2 km:

b. Find an expression for r² in terms of t

c. Find the time, in days and hours to the nearest hour, after which the radius of the spill is 1.5 km.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Pearson Edexcel A Level Mathematics Pure Mathematics Year 2

ISBN: 9781292183404

1st Edition

Authors: Greg Attwood, Jack Barraclough, Ian Bettison, David Goldberg, Alistair Macpherson, Joe Petran

See More Books

Question Posted: Aug 20, 2023 08:41 AM

See More Questions

As noted in the text, top management of BP adopted a lax approach to safety in its aggressive pursuit of oil discovery. Consider two alternative safety stances it could have adopted. Emulating Exxon...
The rate of change of the oxygen level (in mmol/l) per month in a body of water after an oil spill is given by where t is the number of months after the spill. What function gives the oxygen level P...
A spherical balloon is being inflated. Find the rate of increase of the surface area (S = 4r2) with respect to the radius r when is (a) 1 ft, (b) 2 ft, (c) 3 ft. What conclusion can you make?
Consider a post office with two employees and a single waiting line. On average, the inter-arrival time is 6 minutes. Standard deviation of inter-arrival time is 3.94 minutes. Average service time is...
On January 1, 2011, the Taylor Company adopted the dollar-value LIFO method. The inventory value for its one inventory pool on this date was $400,000. Inventory data for 2011 through 2013 are as...
Continental AG is a large German supplier of auto parts. Assume that Continental had 62.4 million of prepaid expenses on January 1, 2012. ( stands for euro the European currency.) This item mainly...
When is $W$ in Eq. 10.40 positive, and when is it negative? Is your answer consistent with the definition of positive and negative work given in Section 9.2? Equation 10.40 W = mgh, (10.40)
Mackelprang Inc. is in the initial stages of building the premier planned community in the greater Phoenix, Arizona, metropolitan area. The main selling point will be the communitys lush golf...
18 years ago, I purchased 185 shares of a stock worth $14.25 per share. There was a 2:1 split, a 4:1 split, and a 3:1 split during that time period. Today the stock is worth $1.53 per share. If the...
a. Find x (1 + 2x 2 ) 5 dx. b. Given that y = /8 at x = 0, solve the differential equation dy d.x = x(1 + 2x)5 cos 2y
The diagram shows a sketch of the curve y = f(x), where The region R, shown in the diagram, is bounded by the curve, the x-axis and the lines with equations x = 1 and x = 4. The table below shows the...
The Blue Moon Corporation has ending inventory of $407,534, and cost of goods sold for the year just ended was $4,105,612. What is the inventory turnover? The days' sales in inventory? How long on...
Define, compare and contrast "Delights" and "Tradeoffs" as enablers in Operations Management proficiency through New Product/Service Development and Life cycle as influence on performance objectives.
A(n) 70-g ice cube at O C is placed in 810 g of water at 28 o C. What is the final temperature of the mixture?
A chess board is an 8x8 matrix on which chess pieces are placed. A real chess game has a variety of pieces that have different rules defining how each can move and whom they can attack. For example,...
Please explain and compare and contrast manufacturing and services based on the following factors. Also provide similarities and differences of them. Please provide with some examples. Aggregate...
Discuss the advantages and disadvantages that entrepreneurial firms are most likely to experience if they are first movers? Explain briefly
Draw all the structural and geometric (cis-trans) isomers of C3H5CI.
A company has the following incomplete production budget data for the first quarter: In the previous December, ending inventory was 200 units, which was the minimum required, at 10% of projected...
Refer to Exercise 21.19. a. Find the probability that the x chart does not detect a shift of .75 standard deviation on the first sample after the shift occurs. b. Compute the probability that the x...
The company is considering changing the sampling plan so that 20 components are sampled every hour. What is the average number of units produced until the chart indicates that the process is out of...
Refer to Exercise 21.17. Find the average run length to detect the shift. A firm that manufactures notebook computers uses statistical process control to monitor all its production processes. For one...
Write an explanatory note on the implication of employee's negative past experience on change and how it can affect their commitment and willingness to support further change.
Write a named stored procedure that attempts to delete all the rows from order_details and orders tables when you pass it an order number. If you enter an invalid order_number and no rows were...
The Righter Shoe Store Company prepares monthly financial statements for its bank. The November 30 and December 31, 2024, balances contained the following account information: November 30 Supplies...

An oil spill is modelled as a circular disc with radius r km and area A km

Question:

dA dt = k sin 3π ,0 ≤ t≤ 12

Step by Step Answer:

dA dr drdr dA 1 X d...View the full answer

Pearson Edexcel A Level Mathematics Pure Mathematics Year 2

Students also viewed these Mathematics questions