Northstar

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.

Given the two parabolas:

y = x^2 - 2x + 5 and

y = -x^2/2 + 2x + 1

Find the tangent line(s) common to both parabolas.

Thanks.

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.

I have an Excel workbook with a few tabs. On one of the tabs, the letters across the top for the columns and the numbers down the left side for the rows do not show. How do I get them back again?

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.

Let:

r = radius semicircle

2r = width window

h = height rectangular portion of window

P = perimeter window

A = area window

L = amount of light admitted by window

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.

I can’t run YouTube videos anymore. When I try I get the message:

"Hello, you either have JavaScript turned off or an old version of Adobe's Flash Player. Get the latest Flash player."

I have Internet Explorer 8. I have installed the latest Adobe Flash Player. It still doesn’t work. How can I fix it?

What are your favorite tenor arias?

From the origin a line is drawn perpendicular to a tangent of the circle r = 2a cosθ. Find the locus of the point of intersection.

I am interested in a derivation of the answer.

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.

A line segment of length 2a slides with its ends on the x and y-axes. Find the polar equation of the locus described by the point P(r, θ) at which the perpendicular from the origin intersects the moving line.

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:

AA

AAA

AAAA

C

D

Why are there no single A batteries or B batteries?

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.

http://s449.photobucket.com/albums/qq219/ansel_one...

I came up with this completely by accident when I was working on something entirely different.

How do you create a diagram to illustrate a geometry question and post it? The links I’ve seen on other questions seem to be to either photobucket or tinypic.

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.

Calculate the integral ∫arctan(x) dx.

I know the answer because I can look it up in the table of integrals at the back of a calculus book, but I am drawing a blank trying to work it out.

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.

The velocity of a certain particle moving along the x-axis is proportional to x. At time t = 0 the particle is located at x = 2 and at time t = 10 it is at x = 4. Find its position at t = 5.