FIGURE 140 car rental costs at competing agencies. EXERCISES 1.4 length of one s
ID: 2874741 • Letter: F
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FIGURE 140 car rental costs at competing agencies. EXERCISES 1.4 length of one sides. Draw the graph, and area estimate the dimensions of the field of maximum 1. The product of two numbers is 318. Express the sum of the numbers as a function of the smaller 8. NG A closed box with a square base is to have a volume of 1.500 cubic inches. Express its 2. The sum of two numbers is 18. Express the product surface area as a function of the length of its base. of the numbers as a function of the smaller number. 9. PACKAGING A closed box with a square base has POPULATION GROWTH In the absence of a surface area of 4,000 square centimeters. Express environmental constraints, population grows at a its volume as a function of the length of its base, rate proportional to its size. Express the rate of radium population growth as a the size of the 10. RADIOACTIVE DECAY A sample of of function of the amount decays at a rate proportional to 4, LANDSCAPING A landscaper wishes to make radium remaining. Express the rate of decay of a rectangular flower garden that is twice as long the sample as a function of the amount remaining. as it is wide. Express the area of the garden as a 11. TEMPERATURE CHANGE The rate at which the temperature of an object changes is proportional function of its width to the difference between its own temperature and 5. FENCING A farmer wishes to fence off a of the surrounding medium. rectangular field with 1.000 feet of fencing. If the Express this rate as a function of the temperature long side of the field is along a stream (and does not require fencing), express the area of the field 12. SPREAD OF AN EPIDEMIC The rate at as a function of its width which an epidemic spreads through a community 6. FENCING A city recreation department plans is jointly proportional to the number of people to build a rectangular playground 3.600 square who have caught the disease and the number who meters in area. The playground is to have not. Express this rate as a function of the by a fence. Express the length of the number of people who have caught the disease. fencing as a function of the length of one of the sides of the playground, draw the graph, and 13. POLITICAL CORRUPTION The rate at which estimate the dimensions of the playground mplicated in a government scandal is requiring the least amount of fencing jointly proportional to the number of people 7, AREA Express the area of a rectangular already implicated and the number of people whose perimeter is 320 meters as a function of the involved who have not yet been implicated.Explanation / Answer
1) Let two numbers be x and y where x is smaller
xy = 318 => y = 318/x
Sum , S(x) = x + y = x + (318/x)
3) Let size of Population be x
=> dx/dt = kx , where k is constant of proportionality
5) Let long side be l and width be w
One of the long side does not require fencing
=> l + 2w = 1000 => l = 1000 - 2w
Therefore , Area , A = l * w = (1000 - 2w) * w
9) Let length of square base be 'a' and height be 'b'
=> Surface Area , S = 2a2 + 4ab = 4000
=> b = (4000 - 2a2)/4a
Volume , V = a2b = a2 . ( (4000 - 2a2)/4a ) = (4000a - 2a3)/4
11) dT/dt = k(T - T0)
where k is constant of proportionality and T0 is surrounding temperature
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