#$&* course Mth 158 3/31/13 Around 6:00 PM 027. `* 27
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Given Solution: * * ** P = (x, y) is of the form (x, x^2 - 8). So the distance from P to (0, -1) is sqrt( (0 - x)^2 + (-1 - (x^2-8))^2) = sqrt(x^2 + (-7-x^2)^2) = sqrt( x^2 + 49 - 14 x^2 + x^4) = sqrt( x^4 - 13 x^2 + 49). ** What are the values of d for x=0 and x = -1? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: d(0) = sqrt(0^4 - 13(0)^2 + 49) = sqrt(49) = 7 d(-1) = sqrt((-1)^4 - 13(-1)^2 + 49) = sqrt(1 - 13 + 49) = sqrt(37) roughly = 6.08 confidence rating #$&*: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: * * 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( 63). sqrt(64) = 8, so sqrt(63) is a little less than 8 (turns out that sqrt(63) is about 7.94). 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 verify that these distances make sense. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I don't think the answer to d(-1) is sqrt(63). The part in the given solution: sqrt((-1)^4 - 13 * (-1) + 49), should read: sqrt((-1)^4 - 13 * (1) + 49), I think. -1 squared is positive 1 not negative. ------------------------------------------------ Self-critique Rating: 2
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Given Solution: * * ** 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. ** What is the expression for perimeter p as a function of the radius r of the circle? The perimeter of the square is 4 times the length of a side which is 4 * 2r = 8r. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: * 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. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: I am at a loss for this problem, I don't know where to start. I am mostly confused on how to structure the equation, if I knew that, I might be able figure it out from there. confidence rating #$&*: 1 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: * * ** 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). ** qa college algebra part 2 030. * 30 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I did not know what to do with the information I was given. I see how, in the given solution, the answer was gotten, but just am not sure how I would know to do some of that. I have no idea how 2 + 30t and 3 + 40t give the ""position function"". I understand that it is the distance from the intersection plus their speed multiplied by time, but I don't know how I would know to format it that way. Also, if I am correct, you are using the intersection as the origin which gives us: Distance formula: sqrt(x - 0)^2 + (y - 0)^2) = sqrt(x^2 + y^2) And then you are replacing x and y with the two position functions to express the distance between the two as a function of time. If I knew why the 2 + 30t and 3 + 40t were formatted how they are, I think I would've been able to get it. ------------------------------------------------ Self-critique Rating: 1