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I needed some help with my Calculus homework. The teacher gave our class some problems which i have no idea how to start. If someone can tell me how to start the questions or how to approach at solving it... it'll be greatly appreciated. Though I gave my some thoughts. let me know if im correct/wrong....

Question One

Video tape is unwounded from a spool at a constant rate of 10'' per second. If the tape is 0.02'' thick, how fast is the radius of the spool decreasing when the radius is 2'' ?

** The is a related rate problem so I tried solving or at least started out by first figuring out what formula to use and I think its the sphere volume formula --- V=(4/3)(pie)(r^2). The rate is given 10'' per second and the radius is given too - 2''. I tried plugging in the numbers and taking 1st derivative but that don't seem right or is that how it should be started? Plz help me with this one.

Question Two

Show that the general cubic curve Y = ax^3 + bx^2 + cx + d has one inflection point and three possible shapes depending on whether b^2 > 3ac, b^2 = 3ac or b^2 < 3ac.

** What I did for this question was that I took the 2derivative and got y'' = 6x + 2 (assuming the letters, a-b-c-d are all one coefficients). Then I set the 2nd derivative equal to zero and solved for the possible points of inflections. I then tested (-1) and (1) points from the intervals ( neg. infinity to -1/3) and (-1/3 to pos. infinity) and saw that there is a sign change from negative to positive so therefore there exisits one point of inflection which is x = -1/3.

** I dont know how to do the 2nd part. Not sure where to start and how to show the shapes.

Question Three

If a ray of light emanating from a point A above a horizontal mirror is reflected to a point B above the mirror, show that under the assumption that the light travels by the path of least time, and hence of shortest distance, the angle of incidence is equal to the angle of reflection by using calculus to minimize a function giving the distance. There is a more elegant, purely geometric demonstration for this result.

** There are no numbers here so I dont know what to do. The question itself is confusing to me. Again, plz help me with this one too.

Any help to either of these questions will be great.

thanks in advance

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# Homework Help: Calculus HW Help

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