Given a right circular cylinder with
V = volume
r = radius
h = height
S = surface area
What is the value of h in terms of r that will minimize the surface area?
This is an easy problem with calculus but I found it in a high school precalculus book.2 AnswersMathematics7 years ago
How do I create a folders in a library (in this case Documents)? I only seem to have the option of adding already existing folders. I need to create them and put files in them. I had them before but some folders were accidentally deleted. I have a copy on an detachable external drive but can't figure out how to put a copy of them back on my computer.
In older versions of windows this used to be so easy. Now I can't get Windows to do much of anything
Thanks for your help.1 AnswerSoftware8 years ago
For the curve with parametric equations
x = a[t – sin(t)]
y = a[1 – cos(t)]
find the following quantities.
(a) The area bounded by the x-axis and one loop of the curve
(b) The length of one loop
(c) The area of the surface of revolution obtained by rotating one loop about the x-axis
(d) The coordinates of the centroid of the area in (a)
I thought I knew how to do this problem, but the answer in the back of the book disagrees.
A Norman window has the shape of a rectangle surmounted by a semicircle. If the rectangle is made of clear glass while the semicircle is made of colored glass which transmits only half as much light per square unit as the clear glass does, what are the dimensions of the window that will admit the most light for a given perimeter. Solve for the width of the window and the height of the rectangular portion of the window in terms of the perimeter.
r = radius semicircle
2r = width window
h = height rectangular portion of window
P = perimeter window
A = area window
L = amount of light admitted by window3 AnswersMathematics1 decade ago
Find parametric equations for the locus of points in a plane for the data given.
d²x/dt² = - dx/dt
dy/dt = x
t = 0; x = 1; y = 1; dx/dt = 1
A shell is projected with initial velocity v at an angle α to the horizontal from a point that is at the foot of a hill inclined with angle φ to the horizontal, where
0 < φ < α < π/2
Find the distance to where the shell reaches the ground measured up the face of the hill.
And find the angle α, that achieves maximum range for a given initial velocity v.6 AnswersPhysics1 decade ago
I can’t run YouTube videos anymore. When I try I get the message:
I have Internet Explorer 8. I have installed the latest Adobe Flash Player. It still doesn’t work. How can I fix it?2 AnswersYouTube1 decade ago
Given a triangle in which the bisector of one angle also bisects the opposite side, prove that the triangle is isosceles.
Let's label the sides to make it easier to talk about. In triangle ABC the bisector of angle A also bisects the opposite side BC at point D.
I recently saw AAAA 1.5V batteries on sale at the store. I haven’t seen batteries this small before. What are they used for? This piqued my curiosity about another thing also. We have 1.5V batteries in sizes:
Why are there no single A batteries or B batteries?5 AnswersOther - Electronics1 decade ago
You have a fixed circle O with a point P on the circumference. Point P is the center of circle P. Point Q is on the circumference of circle P. As point P moves around circle O, point Q traces out a curve. Circle P remains tangent to the line y = -a as point P moves around circle O. Circle O is tangent to the same line.
What is the equation and nature of the curve traced out by point Q? Prove or disprove that it is an ellipse. Please see the link for an illustration.
I came up with this completely by accident when I was working on something entirely different.
Suppose I have a tilted ellipse represented by the equation:
4x² + 16xy + 25y² + 8x – 20y + 4 = 0
If after some number crunching I get:
(x + 2y + 1)²/9 + (y – 2)²/4 = 1
Can I then take the area of the ellipse to be:
Area = πab = π*3*2 = 6π
I’m inclined to think this works, but don’t know how to prove or disprove it. I’m looking for an explanation in addition to an answer. Thanks.4 AnswersMathematics1 decade ago
How many different commutative binary operations can be defined on a set of:
i) two elements
ii) three elements
iii) n elements
I can see the answers in the back of the book are 8, 729 and
n^[n(n+1)/2], respectively, but don’t know how they got them.