Write the equation of the line tangent to this graph at the point (-1, 0). After
ID: 2868792 • Letter: W
Question
Write the equation of the line tangent to this graph at the point (-1, 0). After insulting Ms. Keith, Mr. Murphy realises his life is in danger. Mr. Murphy, smarter than the average bear, builds a dummy, with a round thick-skinned balloon ( known as an inflated sphere to NRCC calculus students) for the head, to sit in his own seat while he attempts an escape through the AC ductwork. Ms. Keith, seeking revenge, stabs the head of the dummy with her pencil and tehn begins to laugh. With the pencil left in teh head, teh balloon begins to deflate at a rate of -25 in 3 / sec. How fast is the radius decreasing when the radius is 3 in?Explanation / Answer
2 . dv / dt = - 25 in^3 / sec
r = 3in ; dr / dt = ?
v = 4/3 * pi * r^3 = volume of sphere.
differentiating on both sides wrt "t" .
dv/dt = 4/3 * pi * (3r^2 ) * dr / dt
-25 = 4/3 * pi * (3*3^2) *dr/dt
-25 = 4/3 *pi * (3*9) *dr/dt
-25 = 4/3 * pi * (27) * dr /dt
-25 = 4 * 9 * pi *dr / dt
- 25 = 36 * pi *dr / dt
-25/(36*pi) = dr/dt
-25 * 7 / ( 36 * 22 ) = dr / dt = - 0.22 in / sec .
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