Recent Homework Questions About Calculus
A piece of wire 40 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How much of the wire should go to the square to minimize the total area enclosed by both figures?
Monday, November 18, 2013 at 8:08pm
A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus, the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 25 ft, find the dimensions of the window so that the greatest possible amount of light is ...
Monday, November 18, 2013 at 8:07pm
The top and bottom margins of a poster are 2 cm and the side margins are each 4 cm. If the area of printed material on the poster is fixed at 386 square centimeters, find the dimensions of the poster with the smallest area.
Monday, November 18, 2013 at 8:06pm
10x−6y√(x^2+1)dy/dx=0 6y√(x^2+1) dy/dx = 10x 6y dy = 10x/√(x^2+1) dx 3y^2 = 10√(x^2+1) + c Since y(0) = 4, 3*16 = 10+c c = 38 now you have it.
Monday, November 18, 2013 at 1:55pm
I did plot the curve on Wolfram and got full curve across 3pi. Curve length is also shown full at 3pi but period is shown as 6pi.I can't understand this.
Monday, November 18, 2013 at 12:18am
f is a function from R to R such that f(a) is rational when a is irrational and f(a) is irrational when a is rational . prove that f cannot be continuous
Sunday, November 17, 2013 at 6:52pm
since the curve is a parabola, there is no inflection point. Since #1 #2 do not provide any useful data, the other items are hard to figure.
Sunday, November 17, 2013 at 5:27pm
ohaganbooks is offering a wide range of online books, including current best-sellers. a colleague has determined that the demand for the latest best selling book is given by q=(-p^2)+33p+9 (18<p<28) copies sold per week when the price is p dollars. can you help me ...
Sunday, November 17, 2013 at 4:59pm
Calculus - Optimization
if the expensive side is x and the other dimension is y, then the cost c is c = 4(x+2y) + 12x But, we know the area is xy=800, so y = 800/x and the cost is now c = 4(x+1600/x) + 12x minimum cost when dc/dx=0, so we need dc/dx = -16(400-x^2)/x^2 dc/dx=0 when x=20, so the fence ...
Sunday, November 17, 2013 at 3:38pm
(a) time = distance/speed, so a trip of 1000km takes 1000/v hours. So, the cost is c(v) = (1000/v)(160 + 1/100v^3) (b) Now just find minimum cost where dc/dv = 0 dc/dv = 20(v^3-8000)/v^2 so minimum cost when v=20 (c) Since min occurs at v=20, if top speed is 16, then minimum ...
Sunday, November 17, 2013 at 8:37am
time to go a distance d is d/v so the cost is (d/v)(kv^3) = dkv^2 Looks like k=0 makes cost=0. I suspect a typo.
Sunday, November 17, 2013 at 8:33am
thanks...though I asked for (-3,-1).
Sunday, November 17, 2013 at 2:31am