Poincare's model of Lobachevskian geometry was to say that points of the plane are represented by points in the interior of a circle

Poincare's model of Lobachevskian geometry was to say that points of the plane are represented by points in the interior of a circle and lines by both the diameters of the circle and the arcs of circles orthogonal to it. Draw a diagram(s) to illustrate his model and explain his theory.

Lobachevsky - Write a brief description of Lobachevsky's geometry.

Write a brief description of Lobachevsky's geometry.

Postulates in Geometry - Through 2 points in a circle, there is exactly one arc of a circle orthogonal to it. What basic postulate does this illustrate?

Through 2 points in a circle, there is exactly one arc of a circle orthogonal to it. What basic postulate does this illustrate?

Please see the attached file for the question.

Please see the attached file for the question.

Pentagon - Please see attached file for the question.

Please see attached file for the question.

Sequences, Induction & Binomial Theorem

Please show me the step wise solution for each section of this question. Please see both attachments. Second attachment has the third section of this question.

Finding gradient vector and equation of tangent plane of a given function at a point.

Consider the function f(x,y)=∜(x^2+y^2 ) Find the gradient vector of the function at the point (1, 1). Find the equation of the tangent plane at the point (1, 1) I’ve tried to solve the gradient vector of the function by trying to differentiate the x and y values of the unction. I’m just unsure how to do this when ...continues

A fireplace arch is to be constructed in the shape of a semi ellipse. The opening is to have a height of 40 inches at the center and a width of 82 inches along the base. To sketch the outline of the fireplace, the contractor uses a 82-inch string tied to two thumbtacks. Where the thumbtacks should be placed. Answers 1. 21 inches on either side of the center 2. 7 inches on either side of the center 3. 20 inches on either side of the center 4. 9 inches on either side of the center

A fireplace arch is to be constructed in the shape of a semi ellipse. The opening is to have a height of 40 inches at the center and a width of 82 inches along the base. To sketch the outline of the fireplace, the contractor uses a 82-inch string tied to two thumbtacks. Where the thumbtacks should be placed. Answers 1. 21 in ...continues

Judy and Pete are building a new house and want to carpet their living room

Please see the attached file. 1. Judy and Pete are building a new house and want to carpet their living room, except for the entrance way and the semicircle in front of the fireplace that they want to tile (Alexander & Koeberlein, 2003). A. How many square yards of carpeting are needed? (Hint: There are 9 square feet ...continues

Geomotry problems

Please see attached. Thanks for your help! 1. Along a straight shoreline, two lighthouses, A and B, are located 2000 feet apart. A buoy lies in view of both lighthouses, with angles 1, 2, and 3 as indicated. (Angle 1 is denoted by , angle 2 is denoted by , and angle 3 is denoted by .) 2. The two parallel lines a and b ...continues