course Mth 158
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17:35:21 query 3.6.2 / 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 --> d =sqrt (x-0)^2 +( y -(-1) )^2 d =sqrt x^2 + (y +1)^2 d(x) = sqrt x^2 + (0^2 - 7)^2 d(0) = sqrt 0^2 + (0^2 - 7)^2 = 0 + 49 = 49 d( -1) = sqrt ( -1)^2 +( ( -1 )^2 + ( ( -1) - 7)^2 = sqrt 1 + ( -6)^2 = sqrt 37
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17:40:31 ** 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 don't understand. I have saved the solution on my work page and will try to figure out your solution.
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17:50:53 What are the values of d for x=0 and x = -1?
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RESPONSE --> x(o) = sqrt 0^2 - (-13)0^2 +49 = 7 x(-1) = sqrt ( -1)^4 - ( 13)(-1)^2 +49 = sqrt 1 - (13) + 49 = sqrt 37
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17:53:09 ** 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 see my computation error.
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17:55:35 query 3.6.9 / 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 --> A (x) = 2x * 2y = 2x * 2sqrt-x +4
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18:28:17 ** 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 ok
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18:31:58 What is the expression for perimeter p as a function of the radius r of the circle?
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RESPONSE --> the primeter of a square is 4s. the diameter of the circle is 4 * 2r. then if x = the radius, then P(x) = 4(2x) or 8x.
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18:32:08 ** The perimeter of the square is 4 times the length of a side which is 4 * 2r = 8r. **
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RESPONSE --> ok
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19:06:05 query 3.6.19 / 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 --> d^2 = ( d1)^2 +) ( d2)^2 d^2 ( 2 - 30t^2) + ( 3- 40t^2) d^2 = sqrt 4 -120t +900t^2 240t + 1600t^2 d = sqrt 2500t^2 -360t + 13
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19:06:24 ** 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 --> ok
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