course Mth 152 yfɝᯋefassignment #022
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21:01:55 **** query 9.3.12 area of parallelogram **** What is the area of the given parallelogram and how did you obtain it?
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RESPONSE --> A = bh A = 4(2.5) A = 10 in^2
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21:02:33 The formula for the area of a parallelogram is A = bh ( area = base times height) From the figure the base is 4 and the altitude is 2.5 so we have A = 4 * 2.5 = 10. The area is 10 in.
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RESPONSE --> Correct answer.
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21:19:27 **** query 9.3.18 area of trapezoid **** What is the area of the given trapezoid and how did you obtain it?
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RESPONSE --> A = 1/2h(b + B) A = 1/2(3)(4 + 5) A = 1/2(3)(9) A = 13.5 cm ^2
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21:19:57 The formula for finding the area of a trapezoid is A = 1/2h ( b + B ) h = 3, b = 4, B = 5 A = 1/2 (3) (4 + 5) A = 1/2 (3) (9) A = 1/2 (27) A = 13.5 The area is 13.5
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RESPONSE --> Correct answer.
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21:26:14 **** query 9.3.24 dim of rect with lgth 20 more than wdth and perimeter 176 **** What are the dimensions of the rectangle?
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RESPONSE --> P = 2w + 2l 176 = 2w + 2(w + 20) 176 = 2w + 2w + 40 176 = 4w + 40 176 - 40 = 4w + 40 - 40 136 = 4w 34 = w w = 34 l = 54 34 + 34 + 54 + 54 = 176
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21:26:31 ** The perimeter of a rectangle is P = 2l + 2w, where l and w are length and width. From the given information Length = 20 + w Perimeter = 176 This gives us the equation 176 = 2 (20 + w) + 2w which we proceed to solve for w: 176 = 40 + 2w + 2w by the Distributive Law. Simplifying we get 176 = 40 + 4w Subtract 40 from both sides to get 136 = 4w Divide both sides by 4 to get w = 34 l = w + 20 so l = 34 + 20 = 54 We have Length = 54 and Width = 34 Checking, we have perimeter = 2 * length + 2 * width so we should have 176 = 2(54) + 2(34). The right-hand side does give us 176 so the solution checks out. **
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RESPONSE --> Correct answer.
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22:30:53 **** query 9.3.48 trap bases x, x+4 alt 3 area 30 **** What is the value of x?
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RESPONSE --> A = 30 A = 1/2h(b + B) A = 1/2(3)(x + x + 4) 30 = 1.5(2x+4) 30=3x + 6 30-6 = 3x + 6 - 6 24 = 3x x = 8
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22:31:04 The formula for finding the area of a trapezoid is A = 1/2h ( b + B). We have A = 30 h = 3 B = x + 4 b = x 30 = 1/2(3) ( x + x+4) 30 = 1.5 ( x+x+4) 30 = 1.5x + 1.5x + 6 30 = 3x + 6 Subtract 6 from both sides 24 = 3x Divide both sides by 3 x = 8 The answer is 8.
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RESPONSE --> Correct answer.
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22:44:36 **** query 9.3.54 $60 to paint ceiling of 9 x 15 rm, how much to paint if dimensions 18 x 30 **** What is the cost for the second ceiling? **** How did you use the results of exercise 53 to obtain your result?
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RESPONSE --> 9 * 15 = 135 ft. $60/135 = .44 18 * 30 = 540 ft 540 * .44 = $237.60
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22:45:53 The sides doubled from 9 ft. to 18 ft. and from 15 ft. to 30 ft. When the sides are doubled the area increases by a factor of 4. So the cost is $60 * 4 = $240 The cost for the second ceiling is $240
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RESPONSE --> I did not use the results from problem #53. I worked the problem out.
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22:48:12 **** query 9.3.60 triangle alt 9 on top of 10 x 4 rect; parallelogram alt 3 under **** What is the area of the given figure and how did you obtain your result?
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RESPONSE --> A of triangle = 1/2bh A = 1/2(9)(10) = 45 A of rectangle = l * w A = 10 * 4 = 40 A of parallelogram = bh A = 10 * 3 = 30 Area = 45 + 40 + 30 = 115
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22:48:34 ** Here's a solution by a student from a previous semester: I found the area of each figure and then added those three results together. Area of Triangle = 1/2bh A = 1/2 (10) (9) A = 1/2 (90) A = 45 Area of Rectangle = lw A = (10) (4) A = 40 Area of Parallelogram = bh A = (10) (3) A = 30 45 + 40 + 30 = 115 Area = 115 **
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RESPONSE --> Correct answer.
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22:54:11 **** query 9.3.67 26 m diam circle inscribed in sq; area outside circle **** What is the area of the shaded region and how did you obtain it?
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RESPONSE --> A of the square = s^2 A = 26^2 = 676 A of the circle = pi (r)^2 A = 3.14 (13)^2 = 3.14(169)=530.66 676 - 530.66 = 145.34 m^2 (area of shaded region)
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22:54:26 ** The circle has diameter 26 m so its radius is 13 m and its area is A = pi r^2 = pi * (13 m)^2 = 169 pi m^2 = 531 m^2. The area of the square is the square of its side A = (26 m)^2 = 676 m^2. The area of the shaded region is the difference } 676 m^2 - 531 m^2 = 145 m^2. **
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RESPONSE --> Correct answer.
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22:58:09 **** query 9.3.72 10, 12, 14 in pizzas for 11.99, 13.99, 14.99 **** Which pizza is the best buy and how did you
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RESPONSE --> 3.14(5)^2 = 78.5; $11.99/78.5 = .15 3.14(6)^2 = 113.04; $13.99/113.04 = .12 3.14(7)^2 = 153.86; $14.99/153.86 = .10 14-inch pizza for $14.99 is the best buy.
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22:58:29 obtain your result?
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RESPONSE --> 14-inch pizza for $14.99 is the best buy.
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22:58:50 Student Solution: The thickness is about the same for all three pizzas so the amount of pizza can be measured by its area. I therefore found the area of each. A = 3.14 * r^2 and radius is 1/2 the circumference. So we get areas A = 3.14 (5)^2 = 78.5 A = 3.14 (6)^2 = 113.04 A = 3.14 (7)^2 = 153.86 I then divide the prices and these answers to get the price per square inch. $11.99 / 78.5 = 15.3 $13.99 / 113.04 = 12.4 $14.99 / 153.86 = 9.7 Since 9.7 is the least, and since this is the result for the 14 inch pizza, the 14 in. pizza for $14.99 is the best buy.
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RESPONSE --> Correct answer.
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22:58:57 **** Query Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> No surprises.
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