Finding the cubic yard

An engineer's plan shows a canal with a trapezoidal cross section that is 8 ft deep and 14 ft across at the bottom with walls sloping outward at an angle of 45 degrees. The canal is 620 ft long. A contractor bidding for the job estimates the cost to excavate the canal at $1.75 per cu yd. If the contractor adds 10% profit, what s ...continues

Differential Geometry, imbedded submanifold.

Let phi : R^2 --> R be a function given by phi(x,y) = x^3 + xy + y^3 +1 For which points p =(0,0) , p=(1/3,1/3), p =(-1/3,-1/3) is the subset phi^-1 ( phi(p)) an imbedded sub-manifold of R^2. ( This question was given as part of Differential Geometry course, we use Do Carmo's book,Riemannian Geometry) Please ...continues

Differential Geometry/Orientable Manifolds.

This problem is number 3 page 33 of handout chapter 0. I attached the handout for the chapter ( from Do Carmo's Book) and I hope you can solve it using the theorems and the same way Do Carmo does it, which shouldn't be very hard to follow. ( I believe the main idea is just to use the def of the orientable manifolds and show ...continues

Proper affine function

I attached the problem and chapters 2 and 3 ( chapter 3 is about affine connections). Please solve it using the way that the book does it. ( Handouts are from Do Carmo's book).

Vector Fields

(See attached files for full problem description) For this one you need chapter 2 I think, it is problem number 4 page 57.

Word problem

(See attached file for full problem description) The area A of an equilateral triangle varies directly as the square of the length of a side. If the area of the equilateral triangle whose sides are of length 2 cm is (√3) cm2 , find the length s of an equilateral triangle whose area A is (√3)/4 cm2.

Geometry

a- find the measure of one angle in the polygon. round to nearest tenth if needed. 1- regular 30- gon 2- regular 35- gon b- sum of angle and number of sides to polygon sum of angles number of sides to polygon 5040 1800 2160 4140 c- tell whether the stateme ...continues

geometry

(See attached files for full problem description)

Geometry: Finding the angles of Polygons

Find the value of x and any unknown angles. Find the measure of one angle in the polygon. Round to nearest tenth if needed. 4. Regular 30-gon 5. Regular 35-gon For #6-8, find the value of x and any unknown angles For #1-4, use the diagram on the right. 1. Which two numbered angles form a right angle? 2. Which numbe ...continues

geometry

(See attached files for full problem description)