(6) A diagonal of a rectangle in neutral geometry divides the rectangle into triangle I and...

(6) A diagonal of a rectangle in neutral geometry divides the rectangle into triangle I and triangle II. Can the angle-sum of triangle I be less than 180°? Why or why not?

Expert Solution

milcah answered 2 years ago

Find the maximum area of a rectangle inscribed in a triangle of area A.(NOTE: the triangle...

Find the maximum area of a rectangle inscribed in a triangle of area A.(NOTE: the triangle need not necessarily be a right angled triangle).

in the triangle PQR, the point S divides the line PQ in the ratio 1:3, and...

in the triangle PQR, the point S divides the line PQ in the ratio 1:3, and T divides the line RQ in the ratio 3:2. PR =a and PQ =b express the following in terms of a and b PS , SR, and TQ

/* calculating area of a circle, calculating area of a rectangle, calculating area of a triangle,...

/* calculating area of a circle, calculating area of a rectangle, calculating area of a triangle, and quit. */ import java.util.Scanner; public class GeoCalculator { public static void main(String arg[]) { int geoCalc; //number selection of user Scanner get = new Scanner(System.in); //display section. System.out.println("Geometry Calculator"); System.out.println("Please select from the following menu:"); System.out.println("1. Calculate the Area of a Cirlce."); System.out.println("2. Calculate the Area of a Rectangle."); System.out.println("3. Calculate the Area of a Triangle."); System.out.println("4. QUIT"); System.out.println("Please make a selection:...

Use Java (Geometry: point in a rectangle?) Write a program that prompts the user to enter...

Use Java (Geometry: point in a rectangle?) Write a program that prompts the user to enter a point (x, y) and checks whether the point is within the rectangle centered at (0, 0) with width 10 and height 5. For example, (2, 2) is inside the rectangle and (6, 4) is outside the rectangle. (Hint: A point is in the rectangle if its horizontal distance to (0, 0) is less than or equal to10 / 2 and its vertical...

Write a program to calculate the area of four shapes (Rectangle, triangle, circle and square). The...

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State, without proofs all theorems of neutral geometry that permit to construct a midpoint of a...

State, without proofs all theorems of neutral geometry that permit to construct a midpoint of a given segment. State, without proofs all theorems of Euclidean geometry that permit to execute your construction in the Poincare the Model of the Hyperbolic geometry.

Explain what it is a neutral theorem in Euclidean geometry. State & prove both: the theorem...

Explain what it is a neutral theorem in Euclidean geometry. State & prove both: the theorem on construction of parallel lines and its converse. Which one of them is neutral?

4. Let A be the 6*6 diagonal matrix below. For each eigenvalue, compute the multiplicity of...

4. Let A be the 6*6 diagonal matrix below. For each eigenvalue, compute the multiplicity of λ as a root of the characteristic polynomial and compare it to the dimension of the eigenspace Eλ. (x 0 0 0 0 0 0 x 0 0 0 0 0 0 y 0 0 0 0 0 0 x 0 0 0 0 0 0 z 0 0 0 0 0 0 x) 5. Let A be an 3*3 upper triangular matrix with...

Prove or disprove: In a hyperbolic geometry, if any right triangle has its hypoteneuse and one...

Prove or disprove: In a hyperbolic geometry, if any right triangle has its hypoteneuse and one leg congruent (respectively) to the hypoteneuse and one leg of another right triangle, then the two right triangles are congruent.

Use the green rectangle (triangle symbols) to compute total revenue at various prices along the demand curve.

6. Elasticity and total revenue The following graph shows the daily demand curve for bikes in San Diego. Use the green rectangle (triangle symbols) to compute total revenue at various prices along the demand curve. Note: You will not be graded on any changes made to this graph.

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