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Geometry and Topology

Equation of the tangent plane to the central conicoid

Problem 1 Find the equation of the tangent plane to the central conicoid x2 - 4y2 + 3z2 + 2 = 0 at the point (1,2,0). Problem 2 Find whether the plane 2x + 3y + 2z =3 touches the central conicoid 2x2 + 3y2 + z2 = 1 or not.

Postal Restrictions

Postal Restrictions If a box with square cross section is to be sent by the postal service, there are restrictions on its size such that its Volume is given by V= x²(108-4x), where x ist the length of each side of the cross section (in inches). (a) Is V a function of x? (b) If V= V(x), find V(10) and V(20). (c) What rest

Volume of Ellipsoid

Find the volume of the ellipsoid formed by rotating the semi-ellipse (see attached word file) about the x axis.

Geometric Constructions Parallelograms

USING ONLY AN UNMARKED STRAIGHT EDGE AND A COMPASS CONSTRUCT THE FOLLOWING: (A) A RHOMBUS GIVEN: ONE SIDE AND ONE ANGLE (B) A PARALLELOGRAM GIVEN: TWO ADJACENT SIDES AND THE INCLUDED ANGLE (C) A PARALELLOGRAM GIVEN: THE DIAGONALS AND THE ANGLE BETWEEN THEM ********I NEED STEP-BY-STEP INSTRUCTIONS ON HOW TO CONSTRUCT

Orthonormal Bases : Projection

Please see the attached file for full problem description. 1. Let Complex 3-space C^3 be equipped with the standard inner product and let W be the subspace of C^3 that is spanned by u_1= (1, 0, 1) and u_2= (1/3, 1/3, -1/3). Project the vector v= (1, i, i) onto W. Show work. Help: : is the

Vector Geometry: Cross Products and Real Inner Products

Please see the attached file for full problem description. 1.Let u=(1,-1,3) and v=(2,-1,-1) be vectors in Euclidean 3-space R^3. Find a vector orthogonal to the plane of (subspace spanned by) the vectors u and v. Show work. Help: R^3: is Euclidean 3-space

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 cu

Geometry: Angles

Suppose <ABC and<CBD form a linear pair, <CBD and <DBE form a linear pair, and m<CBD=30. A. Draw a figure representing these angles. B. Write a paragraph proof showing that <ABC=<DBE.

Goat on a Rope Problem

A zero dimensional goat is attached by a rope to a point on the perimeter of a circular field (two dimensional). How long should the rope be (in terms of the radius of the field) so the goat can reach and graze exactly half of the grass of the field?

Determining the distance

Joe and Jill set sail from the same point, with Joe sailing in the direction of S4 degree east and Jill sailing in the direction S9 degree west. After 4 hr, Jill 2 mi due west of Joe. How far had Jill sailed?