A pipe is supported by a block and a wall. Find the pipe radius in term of the block height and its distance from the wall.

A block with height "b" is placed a distance "a" from a wall, to hold in place a pipe with radius "R" (The pipe is supported by the wall on the other side - see attached figure). Find the radius "R" in terms of "a" and "b".

Creating the formula to find the dimensions of a cube.

In Metric. Three college students are trapped in deep snow in northern Canada. To survive they must build an igloo using snow large enough for all of them to fit and small enough to not exceed their strength and stamina. Luckily one of them is a math major and quickly formulates the dimensions of the blocks they need to cut out from the hard packed snow. Because he doesnt know what each block will weigh until they cut it, he quickly calculates an igloo built with 200 blocks, and then again with 300 blocks, and 500 blocks to have the dimensions ready to begin construction immediately. He decides that to house all of them quickly the igloo should be 10 meters in diameter and 5 meters... click for more

For the curve , r = ( 2abt, a^2 log t, b^2t^2 ), Show that κ = - τ = 2abt/(a^2 + 2b^2t^2)^2 where κ = curvature of the curve, τ = torsion of the curve

Differential Geometry (II) Curves in Space Curvature of the Curve Torsion of the Curve For the curve: r = ( 2abt, a^2 log t, b^2t^2 ) Show that: κ = - τ = 2abt/(a^2 + 2b^2t^2)^2 where κ = curvature of the curve τ = torsion of the curve

For the curve r = ( √6 at^3, a(1+3t^2), √6 at ), Show that κ = - τ = 1/[a(1 + 3t^2)^2] where κ = curvature of the curve, τ = torsion of the curve .

Differential Geometry (I) Curves in Space Curvature of the Curve Torsion of the Curve For the curve: r = ( √6 at^3, a(1+3t^2), √6 at ) Show that: κ = - τ = 1/[a(1 + 3t^2)^2] where κ = curvature of the curve τ = torsion of the curve

Distance travelled around box problem

An ant is walking around the outside of the cube in "straight" paths (where we define a straight path in this case as one formed by the edges of a cross section created by a plane slicing through the cube). For example, to get from point Q to point R in the picture above on the right, the ant walks along the red path. There are many different straight paths the ant can take, as you can imagine just by slicing the cube with different planes. 1. Describe and find the length of the shortest possible path the ant could take to get from point A to point G. 2. Describe and find the length of the longest path the ant could take to get from A to G. 3. Describe and find the longest possible pa... click for more