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I want to find  the volume contribution x^2+y^2=z and x^2+y^2=2x over xy with Maple.

In a webinar on July 10, 2013, I solved the related rate problem:

Helium is pumped into a spherical balloon at the constant rate of 25 cu ft per min.
At what rate is the surface area of the balloon increasing at the moment when its radius is 8 ft?

A question in the Q&A at the end of the Webinar asked if it were possible to have an animation illustrate the expanding sphere and the rate of change in the surface area thereof. 

I was thinking about the area problem, yet again, and found myself asking the question: why must we go through such elaborate means to get Maple to generate a plot of the region between two (or more curves)? I use the word elaborate to describe any process that would might become overwhelming, for, say a student, to go through to accomplish a task. Anyone with the most basic of backgrounds can understand the area problem, but yet, such an individual might not find it a trivial...

We have a task her that I hope someone can help us with.

The task is to build a steel frame to a tent.  The frame consists of four legs with X length and a rectangle on the top with sides Y and Z.  The lengths are measured in meters.
The volume V=X*Y*Z of the tent has to be 32 m3.  The task is to create the tent so that the total length L of the pipe is minimized to the shortest.

L=4x+2y+2z

Thx for all fast help :D

   ...

1. a)given ∫(0..4)∫(√x..2) of sin(pi)*y^3 dydx, graph the region, R, in the xy plane.

b)Write double integral which reverses the order of integration and then evaluate.

 

2. Find centroid of cardioid of region enclosed by cardioid r=1-sin(theta)

 

3. a)Graph wedge cut from cylinder x^2+y^2=9, and by planes, z=-y, and z=0, and above the xy plane.

b)Write the integral which finds the volume of the wedge and evaluate it.

The new VolumeOfRevolution command in the Student[Calculus1] package has lots of nice features for controlling the output (Riemann sum, 3D plot, animation, inert integral, numerical approximation, ...).

The default colors for the plot are not very appealing. Not only is the pink easily washed out by a projector in a moderately light room, but the detail is missing. To illustrate, consider

with(Student[Calculus1]):
VolumeOfRevolution(2-x^2, x, x=0..1, output=plot );

How to find the volume of the intersection of the sphere {(x, y, z): x^2+y^2+z^2 <= R^2 } and
the set {(x, y, z): |x| <= a, |y| <= a } under the assumptions R > a*sqrt(2) and a > 0?

I have the following problem. Two formulas in three variables represent the costs of algorithms. I want a visual of their ratio, so that I can "see" how their relative performance varies. Here is a simple example. I can analyze this example analytically, but you can't always do that.

R := sum(binomial(n+i*d,n),i=1..k-1);
S := binomial(n+k*d,n);
f := unapply(R/S, n, d, k);
A := Array(1..10,1..10,1..10,f,datatype=float[8]);

I want a 3-dimensional rendering...

Ive tried several commands, but none of them will give me a response

Here are the points im working with:

u = (2, -3, 1), v = (-4, 3, 3), w = (2, 4, 6)

And here are the several commands ive tried to use, with "with(LinearAlgebra), with(geom3d)" implemented before:

1. 

volume([2, -3, 1], [-4, 3, 3], [2, 4, 6], parallelepiped)

> with(plots, display);
> volume;
display(parallelepiped, axes = normal, scaling = constrained, orientation = ...

I need to create an ellipse and an ellipsoid (ellipse in 3D) through code. How would I be able to do this? Can someone please give me an example for each?

 

Also, I will need to create a line for an ellipse and a plane for an ellipsoid that intersect. Would I be able to find the intersecting points? Would I be able to find the function for the curve line that is created when a plane intersects an ellipsoid? Also, how would I find the surface area and volume...

I currently need to cut a sphere into equal parts becuase I am carrying out an investigation for a school assignment. However, I do not know how I can cut the sphere into pieces in Maple, which I have been told it needs to be done through code. I will need to know how I can cut it so I can carry out my investigation by cutting it into different number of pieces. For example, cutting a sphere into half, so one piece would be a hemisphere.

 

Also, I will...

Use a change of variables to find the volume of the solid region lying below the surface f(x,y)=(2y-x)^4sqrt(x+y) and above the parallelogram in the xy=plane with vertices (3,5) (2,6) (10,10) and (11,9)

Graph the 'ice cream cone' formed ny the upper half of the sphere x^2+y^2+z^2=16 and the cone z=sqrt(x^2+y^2) using maple, and find the z-coordinates of its center of mass.

Graph the region insde the one-sheeted hyperboloid x^2+y^2-z^2=9 between z=4 and z= -4 using maple and find the volume of this region

Graph the solid common to the cylinders x^2+z^2=4 and y^2+z^2=4 using maple and find the volume of the region common to the cylinders.

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