Solutions Modeling Dynamics of Life 3ed Adler -Chapter 1.3

1.3.1 Convert the following into the new units. Find 3.4 pounds in grams (1 ounce is 28.35 grams and 1 pound is 16 ounces).
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1.3.2 Convert the following into the new units. Find 1 yard in mm (1 in. is 25.40 mm and 1 yard is 36 in.).
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1.3.3 Convert the following into the new units. Find 60 years in hours (1.0 year ≈ 365.25 days).
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1.3.4 Convert the following into the new units. Find 65 miles per hour in centimeters per second.
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1.3.5 Convert the following into the new units. Find 2.3 grams per cubic centimeter in pounds per cubic foot.
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1.3.6 Convert the following into the new units. Find 9.807 ... (the acceleration of gravity) in miles per hour per second.
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1.3.7 Compute the answers by adding the given quantities. A boy who is 1.34 meters tall grows 2.3 cm.
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1.3.8 Compute the answers by adding the given quantities. After waiting for 1.2 hours for a plane flight, you are told you will have to wait another 17 minutes. What is the total wait?
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1.3.9 Compute the answers by adding the given quantities. You purchase 6 apples that weigh 145 g each, and 7 oranges that weigh 123 g each. What is the total weight if you add the apples to the oranges?
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1.3.10 Compute the answers by adding the given quantities. The density of the apples in the previous problem is ... and the density of the oranges is .... What is the total volume if you add the apples to the oranges?
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1.3.11 Figure out which of the following is larger. The area of a square with side length 1.7 cm or of a disk with radius 1.0 cm.
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1.3.12 Figure out which of the following is larger. The perimeter of a square with side length 1.7 cm or of a circle with radius 1.0 cm.
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1.3.13 Figure out which of the following is larger. The volume of a sphere with radius 100 m or of a 50 cm deep lake with an area of 3.0 square km.
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1.3.14 Figure out which of the following is larger. The surface area of a sphere with radius 100 m or the surface area of a lake with area 3.0 square km.
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1.3.15 Find the dimensions of the following quantities. Pressure (force per unit area)
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1.3.16 Find the dimensions of the following quantities. Energy (force times distance)
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1.3.17 Find the dimensions of the following quantities. The rate of change of the area of a colony of bacteria growing on a plate.
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1.3.18 Find the dimensions of the following quantities. The force of gravity between two objects is equal to ... are the masses of the two objects, and r is the distance between them. What are the dimensions of the gravitational constant G?
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1.3.19 Check whether the following formulas are dimensionally consistent. Distance = rate times time.
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1.3.20 Check whether the following formulas are dimensionally consistent. Velocity = acceleration times time.
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1.3.21 Check whether the following formulas are dimensionally consistent. Force = mass times acceleration.
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1.3.22 Check whether the following formulas are dimensionally consistent. Energy = 1/2 mass times the square of velocity (see Exercise 16 for the units of energy).Reference Exercise 16 Find the dimensions of the following quantities. Energy (force times distance)
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1.3.23 Using the graph of the function g(x), sketch a graph of the shifted or scaled function, say which kind of shift or scale itis, and compare with the original function. ... 4g(x)
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1.3.24 Using the graph of the function g(x), sketch a graph of the shifted or scaled function, say which kind of shift or scale itis, and compare with the original function. ... g ( x ) − 1
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1.3.25 Using the graph of the function g(x), sketch a graph of the shifted or scaled function, say which kind of shift or scale itis, and compare with the original function. ... g ( x /3)
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1.3.26 Using the graph of the function g(x), sketch a graph of the shifted or scaled function, say which kind of shift or scale itis, and compare with the original function. ... g ( x + 1)
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1.3.27 Find the volumes of the following two cartoon trees (drawing a sketch can help) assuming that the height of the first is 23.1 m and that the height of the second is 24.1 m. What is the ratio of the volume of the larger tree to that of the smaller tree? A tree is a perfect cylinder with radius 0.5 m no matter what the height (the volume of a cylinder with height h and radius r is π ...).
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1.3.28 Find the volumes of the following two cartoon trees (drawing a sketch can help) assuming that the height of the first is 23.1 m and that the height of the second is 24.1 m. What is the ratio of the volume of the larger tree to that of the smaller tree? A tree is a perfect cylinder with radius equal to 0.1 times the height.
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1.3.29 Find the volumes of the following two cartoon trees (drawing a sketch can help) assuming that the height of the first is 23.1 m and that the height of the second is 24.1 m. What is the ratio of the volume of the larger tree to that of the smaller tree? A tree looks like the tree in Exercise 27, but with half the height in the cylindrical trunk and the other half in a spherical blob on top. Reference Exercise 27 Find the volumes of the following two cartoon trees (drawing a sketch can help) assuming that the height of the first is 23.1 m and that the height of the second is 24.1 m. What is the ratio of the volume of the larger tree to that of the smaller tree? A tree is a perfect cylinder with radius 0.5 m no matter what the height (the volume of a cylinder with height h and radius r is π ...).
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1.3.30 Find the volumes of the following two cartoon trees (drawing a sketch can help) assuming that the height of the first is 23.1 m and that the height of the second is 24.1 m. What is the ratio of the volume of the larger tree to that of the smaller tree? A tree looks like the tree in Exercise 27, but with 90% of the height in the cylindrical trunk and the remaining 10% in a spherical blob on top. Reference Exercise 27 Find the volumes of the following two cartoon trees (drawing a sketch can help) assuming that the height of the first is 23.1 m and that the height of the second is 24.1 m. What is the ratio of the volume of the larger tree to that of the smaller tree? A tree is a perfect cylinder with radius 0.5 m no matter what the height (the volume of a cylinder with height h and radius r is π ...).
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1.3.31 Find the mass in kilograms of the following objects. A water bed that is 2 m long, 20 cm thick, and 1.5 m wide. The density of water is 1.0 ....
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1.3.32 Find the mass in kilograms of the following objects. A spherical cow with diameter 1.3 m and density 1.3 ....
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1.3.33 Find the mass in kilograms of the following objects. A coral colony of 3200 individuals each weighing 0.45 g.
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1.3.34 Find the mass in kilograms of the following objects. A circular colony of mold with diameter of 4.8 cm and density of 0.0023 ....
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1.3.35 Change the units in the following functions, and compare a graph in the new units with the original units. (Based on Section 1.2, Exercise 45) The number of bees b on a plant is given by b = 2 f + 1 where f is the number of flowers. Suppose each flower has 4 petals. Graph the number of bees as a function of the number of petals.reference Exercise 45 Evaluate the following functions over the suggested range, sketch a graph of the function, and answer the biological question. The number of bees b found on a plant is given by b = 2 f + 1 where f is the number of flowers, ranging from 0 to about 20. Explain what might be happening when f = 0.
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1.3.36 The number of cancerous cells c as a function of radiation dose r is c =r − 4 for r (measured in rads) greater than or equal to 5, and is zero for r less than 5 (as in Section 1.2, Exercise 46). Suppose that radiation is instead measured in millirads (1 rad = 1000 millirads).
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1.3.37 Insect development time A (in days) obeys A =40 − T/2 where T represents temperature in ?C for ?C between 10 and 40 (as in Section 1.2, Exercise 47). Suppose that development time is measured in hours.
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1.3.38 Tree height h (in meters) follows the formula ... where a represents the age of the tree in years (as in Section 1.2, Exercise 48). Suppose that tree age is measured instead in decades.
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1.3.39 Estimate the following. The speed of light in cm per ns (...seconds or one nanosecond) (the speed of light is about 186,000 miles/second). A fast computer takes about 0.3 ns per operation. How far does light travel in the time required by one operation?
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1.3.40 Estimate the following. Estimate the speed that your hair grows in miles per hour. (This problem was borrowed from the book Innumeracy.)
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1.3.41 Estimate the following. The weight of the earth in kilograms. The earth is approximately a sphere with radius 6500 km and density 5 times that of water.
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1.3.42 Estimate the following. Suppose a person eats 2000 Kcal per day. Using the facts that 1 Kcal is approximately 4.2 Kj (a kilojoule is a unit of energy equal to 1000 joules) and 1 watt is one joule per second (a unit of power), about how many watts does a person use?
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1.3.43 Estimate the following. If a movie is about 2 hours long, how many movies could you watch if you spent half your time watching movies for 60 years?
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1.3.44 Estimate the following. The volume of all the people on earth in cubic kilometers. If a large mine is about 3 km across and 1 km deep, would they all fit?
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1.3.45 The following problems give several ways to estimate the number of cells in your body. A cell is roughly a sphere 10 μ m in radius, where 1 μ m is ...m. Using the fact that the density of a cell is approximately the density of water and that water weighs 1 ..., estimate the number of cells in your body.
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1.3.46 The following problems give several ways to estimate the number of cells in your body. A cell is roughly a sphere 10 μ m in radius, where 1 μ m is ...m. Estimate your volume in cubic meters by pretending you are shaped like a board. Pretending that cells are cubes 20 μ mon a side, what do you estimate the number of cells to be by this method?
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1.3.47 The following problems give several ways to estimate the number of cells in your body. A cell is roughly a sphere 10 μ m in radius, where 1 μ m is ...m. The brain weighs about 1.3 kg and is estimated to have about 100 billion neurons and 10 to 50 times as many other cells (glial cells). Is this consistent with our previous estimates?
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1.3.48 The nematode C. elegans is a cylinder about 1 mm long and 0.1 mm in diameter, consisting of about 1000 cells. Are these cells about the same size as the ones in your body?
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1.3.49 The following problems regard tying string or gift wrapping our planet, thought of as a sphere with radius 6500 km. How long a piece of string would be required to go around the equator? If the string were made 1.0 meters longer and stretched out all the way around, how high would it be above the surface? Does the result surprise you?
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1.3.50 How large a piece of shrink-wrap would be required to cover the entire planet? If the wrap were increased in area by1.0 ... and stretched out all around, how high would it be above the surface? Why do you think the result is so different from the previous problem? (Working this out takes a lot of decimal places.)
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