course Phy 121 v±assignment #003
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11:47:53 `q001. There are 10 questions and 5 summary questions in this assignment. What is surface area of a rectangular solid whose dimensions are 3 meters by 4 meters by 6 meters?
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RESPONSE --> The formula to finde the total surface area of a rectangular solid is T=2(lw+lh+hw). 2(3*4+3*6+6*4)=108 meters square. confidence assessment: 3
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11:48:07 A rectangular solid has six faces (top, bottom, front, back, left side, right side if you're facing it). The pairs top and bottom, right and left sides, and front-back have identical areas. This solid therefore has two faces with each of the following dimensions: 3 m by 4 m, 3 m by 6 m and 4 m by 6 m, areas 12 m^2, 18 m^2 and 24 m^2. Total area is 2 * 12 m^2 + 2 * 18 m^2 + 2 * 24 m^2 = 108 m^2.
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RESPONSE --> self critique assessment: 3
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11:51:17 `q002. What is the surface area of the curved sides of a cylinder whose radius is five meters and whose altitude is 12 meters? If the cylinder is closed what is its total surface area?
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RESPONSE --> The formula for the lateral area of a cylinder is L=2*pi*r*h. 2*3.14*5*12=377 meters square. confidence assessment: 3
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11:52:25 The circumference of this cylinder is 2 pi r = 2 pi * 5 m = 10 pi m. If the cylinder was cut by a straight line running up its curved face then unrolled it would form a rectangle whose length and width would be the altitude and the circumference. The area of the curved side is therefore A = circumference * altitude = 10 pi m * 12 m = 120 pi m^2. If the cylinder is closed then it has a top and a bottom, each a circle of radius 5 m with resulting area A = pi r^2 = pi * (5 m)^2 = 25 pi m^2. The total area would then be total area = area of sides + 2 * area of base = 120 pi m^2 + 2 * 25 pi m^2 = 170 pi m^2.
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RESPONSE --> confidence assessment:
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11:54:16 `q003. What is surface area of a sphere of diameter three cm?
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RESPONSE --> The formula for the surface area of a sphere is T=4*pi*r^2. 4*3.14*1.5^2=28.3 cm square. confidence assessment: 3
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11:54:38 The surface area of a sphere of radius r is A = 4 pi r^2. This sphere has radius 3 cm / 2, and therefore has surface area A = 4 pi r^2 = 4 pi * (3/2 cm)^2 = 9 pi cm^2.
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RESPONSE --> self critique assessment: 3
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12:01:22 `q004. What is hypotenuse of a right triangle whose legs are 5 meters and 9 meters?
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RESPONSE --> You would use pythagoreans theorem which states a^2+b^2=c^2 a and b being the legs and c the hypotenuse. 5^2+9^2=106 then take the square root of 106 to get 10.3 meters. confidence assessment: 3
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12:02:03 The Pythagorean Theorem says that the hypotenuse c of a right triangle with legs a and b satisfies the equation c^2 = a^2 + b^2. So, since all lengths are positive, we know that c = sqrt(a^2 + b^2) = sqrt( (5 m)^2 + (9 m)^2 ) = sqrt( 25 m^2 + 81 m^2) = sqrt( 106 m^2 ) = 10.3 m, approx.. Note that this is not what we would get if we made the common error of assuming that sqrt(a^2 + b^2) = a + b; this would tell us that the hypotenuse is 14 m, which is emphatically not so. There is no justification whatsoever for applying a distributive law (like x * ( y + z) = x * y + x * z ) to the square root operator.
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RESPONSE --> self critique assessment: 3
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12:05:30 `q005. If the hypotenuse of a right triangle has length 6 meters and one of its legs has length 4 meters what is the length of the other leg?
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RESPONSE --> Just rearange pythagoreans thereom so that b^2=c^2-a^2. 6^2-4^2=20 then take the square root of 20 to get 4.5 meters. confidence assessment: 3
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12:05:40 If c is the hypotenuse and a and b the legs, we know by the Pythagorean Theorem that c^2 = a^2 + b^2, so that a^2 = c^2 - b^2. Knowing the hypotenuse c = 6 m and the side b = 4 m we therefore find the unknown leg: a = sqrt( c^2 - b^2) = sqrt( (6 m)^2 - (4 m)^2 ) = sqrt(36 m^2 - 16 m^2) = sqrt(20 m^2) = sqrt(20) * sqrt(m^2) = 2 sqrt(5) m, or approximately 4.4 m.
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RESPONSE --> self critique assessment: 3
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12:09:27 `q006. If a rectangular solid made of a uniform, homogeneous material has dimensions 4 cm by 7 cm by 12 cm and if its mass is 700 grams then what is its density in grams per cubic cm?
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RESPONSE --> Its volume would be 4*7*12=336 cubic cm. To get density we would divide grams by cubic cm 700/336=2.1 grams per cubic cm. confidence assessment: 3
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12:10:08 The volume of this solid is 4 cm * 7 cm * 12 cm = 336 cm^3. Its density in grams per cm^3 is the number of grams in each cm^3. We find this quantity by dividing the number of grams by the number of cm^3. We find that density = 700 grams / (336 cm^3) = 2.06 grams / cm^3. Note that the solid was said to be uniform and homogeneous, meaning that it's all made of the same material, which is uniformly distributed. So each cm^3 does indeed have a mass of 2.06 grams. Had we not known that the material was uniform and homogeneous we could have said that the average density is 2.06 grams / cm^3, but not that the density is 2.06 grams / cm^3 (the object could be made of two separate substances, one with density less than 2.06 grams / cm^3 and the other with density greater than 2.06 g / cm^3, in appropriate proportions; neither substance would have density 2.06 g / cm^3, but the average density could be 2.06 g / cm^3).
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RESPONSE --> self critique assessment: 3
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12:13:59 `q007. What is the mass of a sphere of radius 4 meters if its average density is 3,000 kg/cubic meter?
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RESPONSE --> V=4/3*3.14*4^3=268.1 cubic meters. To get mass you have to multiply its volume by its average density 268.1*3000=304247 kg. confidence assessment: 3
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12:17:07 A average density of 3000 kg / cubic meter implies that, at least on the average, every cubic meter has a mass of 3000 kg. So to find the mass of the sphere we multiply the number of cubic meters by 3000 kg. The volume of a sphere of radius 4 meters is 4/3 pi r^3 = 4/3 * pi (4m)^3 = 256/3 * pi m^3. So the mass of this sphere is mass = density * volume = 256 / 3 * pi m^3 * 3000 kg / m^3 = 256,000 * pi kg. This result can be approximated to an appropriate number of significant figures.
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RESPONSE --> I copied down the wrong answer it should have been 804247 kg. self critique assessment: 2
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12:20:59 `q008. If we build a an object out of two pieces of material, one having a volume of 6 cm^3 at a density of 4 grams per cm^3 and another with a volume of 10 cm^3 at a density of 2 grams per cm^3 then what is the average density of this object?
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RESPONSE --> To get the average density you would have to add the two densitys and then divide the total volume of the object by that number. 16/6=2.667 grams per cm^3. confidence assessment: 2
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12:22:48 The first piece has a mass of 4 grams / cm^3 * 6 cm^3 = 24 grams. The second has a mass of 2 grams / cm^3 * 10 cm^3 = 20 grams. So the total mass is 24 grams + 20 grams = 44 grams. The average density of this object is average density = total mass / total volume = (24 grams + 20 grams) / (6 cm^3 + 10 cm^3) = 44 grams / (16 cm^3) = 2.75 grams / cm^3.
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RESPONSE --> I should have added up the total mass and then divided it by total volume to get average density. self critique assessment: 2
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12:29:09 `q009. In a large box of dimension 2 meters by 3 meters by 5 meters we place 27 cubic meters of sand whose density is 2100 kg/cubic meter, surrounding a total of three cubic meters of cannon balls whose density is 8,000 kg per cubic meter. What is the average density of the material in the box?
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RESPONSE --> The weight of the sand is 2100*27=56700 kg and the weight of the cannon balls is 8000*3=24000 kg add those together and the combined weight of the box is 80700 kg. so density is 80700 kg/ 30 cubic meters=2690 kg per cubic meter. confidence assessment: 3
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12:29:22 We find the average density from the total mass and the total volume. The mass of the sand is 27 m^3 * 2100 kg / m^3 = 56,700 kg. The mass of the cannonballs is 3 m^3 * 8,000 kg / m^3 = 24,000 kg. The average density is therefore average density = total mass / total volume = (56,700 kg + 24,000 kg) / (27 m^3 + 3 m^3) = 80,700 kg / (30 m^3) = 2,700 kg / m^3, approx..
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RESPONSE --> self critique assessment: 3
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12:31:56 `q010. How many cubic meters of oil are there in an oil slick which covers 1,700,000 square meters (between 1/2 and 1 square mile) to an average depth of .015 meters? If the density of the oil is 860 kg/cubic meter the what is the mass of the oil slick?
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RESPONSE --> The volume of the oil is 1,700,00*.015=25500 meters cubed. 25500*860=21,930,000 kg of oil. confidence assessment: 3
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12:36:31 The volume of the slick is V = A * h, where A is the area of the slick and h the thickness. This is the same principle used to find the volume of a cylinder or a rectangular solid. We see that the volume is V = A * h = 1,700,000 m^2 * .015 m = 25,500 m^3. The mass of the slick is therefore mass = density * volume = 860 kg / m^3 * 24,400 m^3 = 2,193,000 kg. This result should be rounded according to the number of significant figures in the given information.
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RESPONSE --> I think your answer is wrong first you state the volume is 25500 m^3 but when you solve for mass you use 24400 m^3 which would make the answer 20,984,000 kg. The answer you gave however is right it is just missing a 0. self critique assessment: 0
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12:37:42 `q011. Summary Question 1: How do we find the surface area of a cylinder?
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RESPONSE --> Total surface area=2*pi*r(r+h) confidence assessment: 3
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12:38:25 The curved surface of the cylinder can be 'unrolled' to form a rectangle whose dimensions are equal to the circumference and the altitude of the cylinder, so the curved surface has volume Acurved = circumference * altitude = 2 pi r * h, where r is the radius and h the altitude. The top and bottom of the cylinder are both circles of radius r, each with resulting area pi r^2. {]The total surface area is therefore Acylinder = 2 pi r h + 2 pi r^2.
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RESPONSE --> self critique assessment: 3
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12:38:44 `q012. Summary Question 2: What is the formula for the surface area of a sphere?
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RESPONSE --> 4*pi*r^2 confidence assessment: 3
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12:38:51 The surface area of a sphere is A = 4 pi r^2, where r is the radius of the sphere.
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RESPONSE --> self critique assessment: 3
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12:40:24 `q013. Summary Question 3: What is the meaning of the term 'density'.
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RESPONSE --> The mass of a given volume. confidence assessment: 3
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12:40:47 The average density of an object is its mass per unit of volume, calculated by dividing its total mass by its total volume. If the object is uniform and homogeneous then its density is constant and we can speak of its 'density' as opposed to its 'average density'
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RESPONSE --> self critique assessment: 3
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12:42:28 `q014. Summary Question 4: If we know average density and mass, how can we find volume?
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RESPONSE --> Divide mass by density to get volume. confidence assessment: 3
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12:42:35 Since mass = ave density * volume, it follows by simple algebra that volume = mass / ave density.
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RESPONSE --> self critique assessment: 3
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12:43:01 `q015. Explain how you have organized your knowledge of the principles illustrated by the exercises in this assignment.
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RESPONSE --> It is all in my old technical math book. confidence assessment: 3
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