course Mth 174 If there are any tips to helping me with 6.4 i would like to know. |UޘLWassignment #002
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12:20:06 Query Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> No real surprises. This assignment did not ask me any questions, other than that in the textbook. But I am still in need of practice with interpreting and drawing graphs. I enjoy the problems dealing with acceleration, velocity, and position. We did those in physics.
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12:22:00 Query Section 6.3 #8, ds / dt = -32 t + 100, s = 50 when t = 0
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RESPONSE --> -32t^2 / 2 + 100t + C -16 * t^2 + 100t + C -16(0)^2 + 100(0) + C = 50 C = 50 -16 * t^2 + 100(t) + 50
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12:22:34 What is the solution satisfying the given initial condition?
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RESPONSE --> -16 * t^2 + 100(t) + 50
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12:23:47 What is the general solution to the differential equation?
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RESPONSE --> I am not sure what the answer should be. But from my understanding of the question, my answer is -16 * t^2 + 100(t) + C
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12:31:12 Query Section 6.3 #14 water balloon from 30 ft, v(t) = -32t+40
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RESPONSE --> v(t) = -32t+40 s(t) = -16t^2 + 40t + C Building is 30 feet tall, so s(0) = 30 = C
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12:33:09 How fast is the water balloon moving when it strikes the ground?
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RESPONSE --> The balloon hits the ground when s(t) = 0 s(t) = 0 when t = 3.104 v(3.104) = -32(3.104) + 40 = -59.328 feet/sec
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12:34:54 How fast is the water balloon moving when it strikes the 6 ft person's head?
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RESPONSE --> The balloon hits the person's head when s(t) = 6 6 = -16t^2 + 40t + 30 0 = -16t^2 + 40t + 24 s(t) = 6 when t = 3 v(3) = -32(3) + 40 = -56 feet/sec
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12:35:38 What is the average velocity of the balloon between the two given clock times?
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RESPONSE --> v(1.5) = -8 v(3) = -56 -56 + -8 = -64 -64 / 2 = -32 feet/sec
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12:37:24 What function describes the velocity of the balloon as a function of time?
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RESPONSE --> v(t) = -32 + 40
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12:40:58 Query Section 6.4 #19 (#18 3d edition) derivative of (int(ln(t)), t, x, 1)
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RESPONSE --> I didn't really understand this section of the text. I would guess the derivative of the integral is just the original problem. But i will look over my notes and the answer to this problem and practice again later.
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12:41:00 What is the desired derivative?
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RESPONSE -->
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12:42:04 The Second Fundamental Theorem applies to an integral whose upper limit is the variable with respect to which we take the derivative. How did you deal with the fact that the variable is the lower limit?
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RESPONSE -->
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12:42:08 Why do we use something besides x for the integrand?
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RESPONSE -->
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12:44:59 Query Section 6.4 #26 (3d edition #25) derivative of (int(e^-(t^2),t, 0,x^3)
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RESPONSE --> I'm not sure what to do about the limits. But using the chain rule, the derivative of e^t^2 is 2t * e^(t^2)
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12:45:41 What is the desired derivative?
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RESPONSE --> e ^ (t^2)
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12:46:29 How did you apply the Chain Rule to this problem?
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RESPONSE --> z = t^2 y = e^z z' = 2t y' = e^t 2t * e^(t^2)
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12:46:34 Why was the Chain Rule necessary?
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RESPONSE -->
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