Group+C+Period+6

PICTURES: [|#15][|#9a][|#9b](b and c[|#3 a & b][|#3 c] Welcome Group C period 6!!! You are to complete problems 3, 9, and 15 from Section 4.6. Each person must contribute. Feel free to use the discussion board to bounce ideas off each other.

Problem 3: Part A: Volume = Pi * r^2 * h One then takes the derivative of this equation and make h the variable and r the constant. Use the product rule to separate r and h. So Dv/dt = pi * r^2 * dh/dt + h * 0 Dv/dt = pi * r^2 * dh/dt This is your final answer. Part B: Use the same formula as part A Then take the derivative of the equation but make r the variable and h the constant. Use the product rule once again. So Dv/dt = pi * r^2 * 0 + h * 2 * pi * r * dr/dt Dv/dt = 2h * pi * r * dr/dt This is then the final answer. Part C: Use the same volume formula as before, but now treat h and r as variables. Use the product rule while taking derivative. So Dv/dt = pi * r^2 * dh/dt + 2 * pi * r * h * dr/dt Number 9: Part A: The area for a rectangle is l*w, so take the derivative for the area. Da/dt = l * dw/dt + w * dl/dt Then substitute the given increasing and decreasing values for length and width for the dw/dt and dl/dt so, 12 * 2 + 5 * -2 you get 14 Part B: Doing the same thing derivative wise but finding the perimeter so use p = 2l + 2w, and use product rule. 2 * dl/dt + l * 0 + 2 dw/dt + w * 0 so then one substitutes in the values given. Thus, 2 * -2 + 2 * 2 and answer is 0. Part C: This is for the diagnale (don't judge my spelling, I don't feel like fixing/googling it) use pythagreoum theroem a^2 + b^2 = c^2 take the derivative of that so, 2a * da/dt + 2b * db/dt = 2c + dc/dt One then plugs in their values given, and solve for dc/dt. So, 2 * 5 * 2 + 2 * 12 * -2 = 2 * 13 * dc/dt. If one is freaking about where 13 comes from it comes from the pythagreom theroem where 5^2 + 12^2 = C^2, so solve and C = 13 Problem 15: Using another cyllinder with height of 6 and diameter of 3.800. Then the radius is increasing .001 in per second. Use the product rule and h ends up being a constant because it is not changing at all. So take derivative, Dv/dt = 2 * pi * r * h * dr/dt. Then plug in one's values given. 2 * pi * 1.9 * 6 * .001/3 and the answer is .0238 in^3/min ] Sorry it took so long.

media type="youtube" key="wBbmchOr_Io" height="315" width="420"media type="youtube" key="ncztcU9EeP0" height="315" width="420"media type="youtube" key="GipmLp86mBg" height="315" width="420"