In my calculus book, the method of increments is used to find the derived function of the product and quotient of two functions. For example for the derivative of the product of functions u and v where u0 and v0 are the values of u and v at x = x0:
y = uv
y' = u0(dv/dx) + v0(du/dx) +...
Homework Statement
A cable weighing 2 pounds per foot of length (and so having a mass of 2 pounds per foot) is suspended from the top of a well 200 feet deep and extends to the bottom. Find the work done in raising the cable to the surface. Over the distance of 200 feet you may use 32m as the...
tim, I tried the formula you mentioned but couldn't obtain the correct answer. Maybe I did something wrong. Beaker, it took me a while to figure out your equation, because i kept reading it as CV02/64 = 2V02/64 without paying enough attention to the parenthesis and i was thinking doesn't c just...
Thanks tim and sammy. By the way, the book i am using is Calculus: An intuitive and physical approach by Morris Kline. So I didn't know a lot of these formulas such as the average velocity formula (v0 + vf)/2 or when to use certain formulas. I think he probably intends for people to solve them...
Thanks for the help sammy and everyone else, I finally got there (with the answer pretty much spelled out) :). I can think about as laterally as a brick. I also solved it with the revised equation mentioned by accatagliato. Man that is a LOT of work. I'm surprised I actually solved it without...
Homework Statement
A body is thrown into the air with an initial velocity of v0. What initial velocity is required to double the maximum height previously attained?Homework Equations
The Attempt at a Solution
I found the max height v02/64 at v0 by solving for 't' in the velocity equation when...
Ok,
v1 = ft1
v2 = ft1+ r(t - t1)
s1 = (ft12)/2
s2 = (ft2)/2 + r(t-t1)2/2
s1 + s2 = (ft2)/2 + (ft2)/2 + r(t-t1)2/2
= (2ft2 + rt2 -2rt1t + rt12)/2
t1 = -rt/(f-r)
So I substitute -rt/(f-r) for t1 into the combined distance equation and with the help of an algebra solver I get...
Homework Statement
A train travels dist 's' in 't' secs. It starts and ends at rest. In first part of journey it moves with const accel 'f', and in second part with const decel 'r'. Show that s = [fr/(f + r)]t^2/2 where f & r are accel and decel
Homework Equations
The Attempt at a...
I have just started a calculus book, and I can't figure out how to solve this problem:
Homework Statement
The landing velocity of an airplane (i.e., the velocity at which it touches the ground) is 100 mi/hr. It decelerates at a constant rate and comes to a stop after traveling 1/4 mile...
Just have a few questions about the cause of heart disease and oxidation of fats. I am looking for some studies that relate to the questions if possible.
1. Does saturated fat cause atherosclerosis or is it the oxidized cholesterol that usually accompanies it (as in most cooked animal...