course MTH 158 pyκۂ瘪zԷassignment #003
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16:16:41 R.3.12 (was R.3.6) What is the hypotenuse of a right triangle with legs 14 and 48 and how did you get your result?
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RESPONSE --> Using the Pythagorean Theorem 14^2 + 48^2 = H^2 196 + 2,304 = H^2 2,500 = H^2 Hypoteneuse = 50 confidence assessment: 3
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16:16:53 ** The Pythagorean Theorem tells us that c^2 = a^2 + b^2, where a and b are the legs and c the hypotenuse. Substituting 14 and 48 for a and b we get c^2 = 14^2 + 48^2, so that c^2 = 196 + 2304 or c^2 = 2500. This tells us that c = + sqrt(2500) or -sqrt(2500). Since the length of a side can't be negative we conclude that c = +sqrt(2500) = 50. **
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RESPONSE --> self critique assessment: 3
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16:18:44 R.3.18 (was R.3.12). Is a triangle with legs of 10, 24 and 26 a right triangle, and how did you arrive at your answer?
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RESPONSE --> Yes, because the Pyth. Theorem only applies to right triangles, and it applies to this... 10^2 + 24^2 = 26^2 676 = 676 confidence assessment: 3
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16:18:57 ** Using the Pythagorean Theorem we have c^2 = a^2 + b^2, if and only if the triangle is a right triangle. Substituting we get 26^2 = 10^2 + 24^2, or 676 = 100 + 576 so that 676 = 676 This confirms that the Pythagorean Theorem applies and we have a right triangle. **
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RESPONSE --> self critique assessment:
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16:23:19 R.3.30 (was R.3.24). What are the volume and surface area of a sphere with radius 3 meters, and how did you obtain your result?
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RESPONSE --> Figure out volume using the method V = 4/3 (pi) (r^3) 4/3 * (pi) (3^3) = 4/3 * (pi) * 27 = 36(pi)^3 Figure out surface area using the method S = 4(pi)(r^2) 4 (pi) (3^2) = 4 (pi) * 9 = 36(pi)^2 confidence assessment: 3
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16:23:36 ** To find the volume and surface are a sphere we use the given formulas: Volume = 4/3 * pi * r^3 V = 4/3 * pi * 3^3 V = 4/3 * pi * 27 V = 36pi m^3 Surface Area = 4 * pi * r^2 S = 4 * pi * 3^2 S = 4 * pi * 9 S = 36pi m^2. **
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RESPONSE --> understood self critique assessment: 3
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16:28:56 R.3.42 (was R.3.36). A pool of radius 10 ft is enclosed by a deck of width 3 feet. What is the area of the deck and how did you obtain this result?
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RESPONSE --> Subtract the area of the pool by the area of the deck and pool... A of pool = (pi) 10^2 = 314ft^3 A of deck and pool = (pi) 13^2 = 530.66ft^3 530.66 - 314 = 216.66 A = 216.66ft^3 confidence assessment: 2
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16:29:19 ** The deck plus the pool gives you a circle of radius 10 ft + 3 ft = 13 ft. The area of the deck plus the pool is therefore pi * (13 ft)^2 = 169 pi ft^2. So the area of the deck must be deck area = area of deck and pool - area of pool = 169 pi ft^2 - 100 pi ft^2 = 69 pi ft^2. **
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RESPONSE --> self critique assessment: 3
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16:29:40 005. `query 5
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RESPONSE --> ? self critique assessment: 0
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16:33:09 R.4.36 (was R.5.30). What is the single polynomial that is equal to 8 ( 4 x^3 - 3 x^2 - 1 ) - 6 ( 4 x^3 + 8 x - 2 )?
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RESPONSE --> 8x^3 - 72x^2 - 8 confidence assessment: 2
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16:35:44 ** ERRONEOUS STUDENT SOLUTION: To make this problem into a single polynomial, you can group like terms together. (8-6)+ (4x^3-4x^3) + (-3x^2) + (8x) + (-1+2). Then solve from what you just grouped...2 (-3x^2+8x+1). INSTRUCTOR CORRECTION: 8 is multiplied by the first polynomial and 6 by the second. You can't isolate them like that. Starting with 8 ( 4 x^3 - 3 x^2 - 1 ) - 6 ( 4 x^3 + 8 x - 2 ) use the Distributive Law to get 32 x^3 - 24 x^2 - 8 - 24 x^3 - 48 x + 12. Then add like terms to get 8x^3 - 24x^2 - 48x + 4 **
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RESPONSE --> understood self critique assessment: 2
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16:37:32 R.4.60 (was R.5.54). What is the product (-2x - 3) ( 3 - x)?
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RESPONSE --> 2x^2 - 3x - 9 confidence assessment: 3
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16:37:47 ** Many students like to use FOIL but it's much better to use the Distributive Law, which will later be applied to longer and more complicated expressions where FOIL does not help a bit. Starting with (-2x - 3) ( 3 - x) apply the Distributive Law to get -2x ( 3 - x) - 3 ( 3 - x). Then apply the Distributive Law again to get -2x(3) - 2x(-x) - 3 * 3 - 3 ( -x) and simiplify to get -6x + 2 x^2 - 9 + 3x. Add like terms to get 2 x^2 - 3 x - 9. **
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RESPONSE --> understood self critique assessment: 3
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16:41:15 R.4.66 (was R.5.60). What is the product (x - 1) ( x + 1) and how did you obtain your result using a special product formula?
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RESPONSE --> First multiply both items in the second parethesis by the x in the first... x (x + 1) = x^2 + x then multiply the second parnthesis by the -1 in the first... -1 (x + 1) = -x -1 and add together x^2 + x - x - 1 = x^2 -1 confidence assessment: 3
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16:41:25 ** Starting with (x-1)(x+1) use the Distributive Law once to get x ( x + 1) - 1 ( x+1) then use the Distributive Law again to get x*x + x * 1 - 1 * x - 1 * 1. Simplify to get x^2 +- x - x + - 1. Add like terms to get x^2 - 1. **
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RESPONSE --> understood self critique assessment: 3
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16:43:39 R.4.84 (was R.5.78). What is (2x + 3y)^2 and how did you obtain your result using a special product formula?
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RESPONSE --> Using FOIL... (2x + 3y)(2x + 3y) = 4x^2 + 6xy + 6xy + 9y^2 = 4x^2 + 9y^2 + 12xy confidence assessment: 3
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16:43:54 ** The Special Product is (a + b)^2 = a^2 + 2 a b + b^2. Letting a = 2x and b = 3y we get (2x)^2 + 2 * (2x) * (3y) + (3y)^2, which we expand to get 4 x^2 + 12 x y + 9 y^2. **
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RESPONSE --> understood self critique assessment: 3
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17:51:04 R.4.90 (was R.5.102). Explain why the degree of the product of two polynomials equals the sum of their degrees.
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RESPONSE --> Because when polynomials that are being multiplied have exponents on them, you just add the exponents, not multiply them. confidence assessment: 2
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17:51:22 ** STUDENT ANSWER AND INSTRUCTOR COMMENTS: The degree of the product of two polynomials equals the sum of their degrees because you use the law of exponenents and the ditributive property. INSTRUCOTR COMMENTS: Not bad. A more detailed explanation: The Distributive Law ensures that you will be multiplying the highest-power term in the first polynomial by the highest-power term in the second. Since the degree of each polynomial is the highest power present, and since the product of two powers gives you an exponent equal to the sum of those powers, the highest power in the product will be the sum of the degrees of the two polynomials. Since the highest power present in the product is the degree of the product, the degree of the product is the sum of the degrees of the polynomials. **
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RESPONSE --> understood self critique assessment: 2
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17:51:37 Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> confidence assessment: 2
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