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11:29:01 query 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 --> x = -20 (20) + 500 x = -400 + 500 x = 100 0 <= p <= 100

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11:30:36 ** 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 --> The question asked if 20 units were sold, you would then simply plug in the number into p.

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11:32:40 query 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 --> y = x^2 - 8 for x,y = 0,-1 -1 = (0)^2 - 8 -1 = 0 - 8 d = -8 + 1 d = -7

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11:33:16 ** 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 it wrong, but I don't know where you got the sqrt at??

By the Pythagorean Theorem, the distance between two points is the square root of the two legs forming the triangle whose hypotenuse forms the distance between the points. In other words, this is the distance formula.

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11:33:36 What are the values of d for x=0 and x = -1?

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RESPONSE --> ?

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11:34:04 ** 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 --> you are supposed to use the distance formula. I do get it now.

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11:39:10 query 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 --> A(r) = r + r ?????????

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11:39:31 ** 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 --> instead of r+r it is 2r^2

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11:40:58 What is the expression for perimeter p as a function of the radius r of the circle?

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RESPONSE --> pi r^2 = P

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11:41:10 ** 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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11:44:32 query 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 --> d^2 = d^2 1 + d^2 2 d^2 = (2-30t)^2 + (3 - 40t)^2 d(t) = sqrt( (2-30t)^2 + (3-40t)^2 ) = sqrt ( 4 - 120t + 900t^2 + 9 - 240t + 100t^2) = sqrt ( 2500t^2 - 360t + 13)

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11:44:45 ** 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 --> correct

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You did well on some of these questions, and appeared to understand the solutions on the others. Let me know if you have questions.