course Mth 158 ??O??????E???assignment #027027. `query 27
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14:15:10 3.6.6. x = -20 p + 500, 0<=p<=25 What is the revenue function and what is the revenue if 20 units are sold?
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RESPONSE --> The revenue function is revenue = demand * price= x*p = (-20p + 500)*p = -20p^2 + 500p if p=24 then -20(24^2) +500(24)= r = 408 confidence assessment: 2
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14:15:18 ** revenue = demand * price = x * p = (-20 p + 500) * p = -20 p^2 + 500 p If price = 24 then we get R = -20 * 24^2 + 500 * 24 = 480. **
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RESPONSE --> I got that one right. self critique assessment: 3
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14:17:08 3.6.10. P = (x, y) on y = x^2 - 8. Give your expression for the distance d from P to (0, -1)
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RESPONSE --> Distance = sqrt( 0 - x)^2) + ( -1 - ( x^2 - 8) )^2 = sqrt( x^2 + ( -7 -x^2)^2 = sqrt( x^2 + 49 -14x^2 + x^4) = sqrt( x^4 -13x^2 + 49) confidence assessment: 2
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14:17:28 ** P = (x, y) is of the form (x, x^2 - 8). So the distance from P to (0, -1) is sqrt( (0 - x)^2 + (-1 - (x^2-8))^2) = sqrt(x^2 + (-7-x^2)^2) = sqrt( x^2 + 49 - 14 x^2 + x^4) = sqrt( x^4 - 13 x^2 + 49). **
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RESPONSE --> I got the correct answer. self critique assessment: 3
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14:18:53 What are the values of d for x=0 and x = -1?
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RESPONSE --> If x= 0 then sqrt( 0^4 - 13(0) + 49) = sqrt(49) = 7 If x = -1 the sqrt( (-1)^4 - 13(-1) + 49 )= sqrt( 15 + 49) = sqrt(64) = 8. confidence assessment: 2
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14:19:03 If x = 0 we have sqrt( x^4 - 13 x^2 + 49) = sqrt(0^4 - 13 * 0 + 49) = sqrt(49) = 7. If x = -1 we have sqrt( x^4 - 13 x^2 + 49) = sqrt((-1)^4 - 13 * (-1) + 49) = sqrt( 64) = 8. Note that these results are the distances from the x = 0 and x = 1 points of the graph of y = x^2 - 8 to the point (0, -1). You should have a sketch of the function and you should vertify that these distances make sense. **
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RESPONSE --> I got that one right. self critique assessment: 3
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14:20:40 3.6. 18 (was and remains 3.6.18). Circle inscribed in square. What is the expression for area A as a function of the radius r of the circle?
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RESPONSE --> The circle's radius is r. The square has sides a length 2r and its area is (2r^2) = 4r^2 confidence assessment: 1
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14:22:03 A circle inscribed in a square touches the square at the midpoint of each of the square's edges; the circle is inside the square and its center coincides with the center of the square. A diameter of the circle is equal in length to the side of the square. If the circle has radius r then the square has sides of length 2 r and its area is (2r)^2 = 4 r^2. The area of the circle is pi r^2. So the area of the square which is not covered by the circle is 4 r^2 - pi r^2 = (4 - pi) r^2. **
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RESPONSE --> I got the area of the square and I know that the area of a circle is pir^2. I didn't know I was supposed to find the area of the square not covered by the circle. I understand how to find it by subtracting the area of the circle from the area of the square. self critique assessment: 2
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14:22:46 What is the expression for perimeter p as a function of the radius r of the circle?
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RESPONSE --> The perimeter of the square is four times the length of a side which is 4 * 2r = 8r confidence assessment: 3
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14:22:52 The perimeter of the square is 4 times the length of a side which is 4 * 2r = 8r. **
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RESPONSE --> I got it. self critique assessment: 3
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14:25:43 3.6.27 (was 3.6.30). one car 2 miles south of intersection at 30 mph, other 3 miles east at 40 mph Give your expression for the distance d between the cars as a function of time.
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RESPONSE --> The function for the first car is 2 + 30t and the function for the other is 3+ 40t. So the distance between the cars is D= sqrt( (2 + 30 t )^2) + ( ( 3 + 40t)^2) sqrt ( 4 + 120t + 900t+ 9 + 240t + 1600t^2 = sqrt( 2500t^2 + 360t + 13) confidence assessment: 2
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14:25:53 At time t the position of one car is 2 miles south, increasing at 30 mph, so its position function is 2 + 30 t. The position function of the other is 3 + 40 t. If these are the x and the y coordinates of the position then the distance between the cars is distance = sqrt(x^2 + y^2) = sqrt( (2 + 30 t)^2 + (3 + 40t)^2 ) = sqrt( 4 + 120 t + 900 t^2 + 9 + 240 t + 1600 t^2) = sqrt( 2500 t^2 + 360 t + 13). **
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RESPONSE --> I got it. self critique assessment: 3
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