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Shortest Path Problem

1 a. Three cities are at the vertices of and equilateral triangle of unit length. Flying Executive Airlines needs to supply connecting services between these three cities. What is the minimum length of the two routes needed to supply the connecting service? 1 b. Now suppose Flying Executive Airlines adds a hub at the "cen

Geometry Application Word Problems

Geometry has many practical applications in everyday life. Estimating heights of objects, finding distances, and calculating areas and volumes are commonplace. One of the most fundamental theorems in geometry, the Pythagorean Theorem, allows us to make many of these calculations. The Pythagorean Theorem states that the square of

Equation of a line Given Two Points and Area of a Triangle

A. Find an equation of a stright line passing through the points with coordinates (-1, 5) and (4, -2), giving your answer in the form ax + by + c = 0 , where a, b and c are integers. b. The line crosses the x-axis at the point A and the y-axis at the point B, and the O is the origin. Find the area of the triangle OAB.


A person who is 6 foot tall walks away from a 40 foot tree towards the tip of the tree's shadow. At a distance of 10 feet from the tree the persons shadow begins to emerge beyond the tree's shadow. How much further must the person walk to completely be out of the tree's shadow?

Volume of a Tetrahedron

Find the volume of a tetrahedron with height h and base area B. Hint: B=(ab/2)sin(theta) Also, please see the attached document for the provided diagram of the tetrahedron.

Fibonacci Sequence Proofs, Pascal's Triangle and Binomial Coefficients

Practice problem 1 Fn is the Fibonacci sequence (f0 = 0, f1 = 1, fn+1 = fn + fn-1). By considering examples, determine a formula for the following expressions, and then verify the formula. a. f0 + f2 + f4 + ...+f2n b. f0 - f1 + f2 - f3 + ...+(-1)n fn --------------------------------------------- Practice proble

Geometric Series : Infinite Series of Circles inside Equilateral Triangles

An equilateral triangle is inscribed in a circle of radius 100. The area of the circle which lies outside of the triangle is shaded. The process continues to infinity. What is the radius for the second area/ third area/ fourth area? Side of first area/ side of second area/ side of third area/ side of fourth area? Area

Word Angle Problem

Find the sum of the measures of the five acute angles that maup up this star...... OK so for this I noticed the 5 triangles that make up the star so i multiplied 180 x 5=900 Then to get the acute angles I did 180/5 and got 36... So the triangle measure would be 72 + 72 +36=180 Acute angles = 36....??? Second pro


In Triangle Rst, medians RM, SN, and TP are congruent at point E What is the point E called? - I think it;s the centroid If Re=24 find RM. 24 (2/3)= 16 Did I do this problem correctly? Im not sure if i multiply by 1/3 or 2/3... The second part follows.... Ab is a chord of circle Q and ab=16cm. Radius QC is pe

45-45-90 Triangles : Length of Hypotenuse

1. In a 45-45-90 triangle, the length of each leg is 18. Find the exact length of the hypotenuse. 2. In the 45-45-90 triangle, the length of the hypotenuse is 20m. Find the EXACT length of each leg.

Prove the Theorem of the Broken Chord

The theory of the broken chord asserts that if AB and BC make up a broken chord in a circle, where BC > AB and if M is the midpoint of arc ABC, the foot F of the perpendicular from M on BC is the midpoint of the broken chord ABC.

Equations of Lines and Intersections

The diagram below (see attachment) shows a triangle ABC whose vertices are at A (-1, 3), B (6, 5) and C (8, -3). The line BP is perpendicular to the line AC, and M is the midpoint of BC. Note that BP is called an altitude of triangle ABC and that AM is called a median of triangle ABC. a) Find the gradient of i) The


How do I go about finding the area of triangle ACE in the following: In rectangle ABDF the following is given: AB=24 BC=7 AF=16 E is the midpoint of FD

Geometery : Volume of Cubes and Area of Triangle

A large cube is 2 feet on each edge. How many cubes - one inch on each edge- will it take to fill the large cube? If the base of a triangle is increased by 20% and the altitude to that base is decreased by 40% then by what percent is the area changed? Is that an increase or a decrease? Decrease by 30%. Is this correct?

Equitlateral Triangles within a Closed Area

(a) Figure 1 shows a closed area ABCDEF in which ABDE is a rectangle and BCD and AFE are equilateral triangles. AE x cm and AB y cm. (i) Find, in terms of x andy, a formula for the area enclosed by the figure ABCDEF and a formula for the perimeter ABCDEF. (ii) Find the minimum perimeter (to two decimal places) of ABCDEF enclos

Solve for beta

In the attached problem, I am trying to solve for Beta. We have done other problems that solve for the faces of the triangle but not sure on how to solve for this face.

Right triangles

1) For the given triangles, a = 14.5m, b = 6.03m and alpha = 55.6 degrees. Find theta. Answer in units of degrees. No picture, but use points (0,0), (5,0), (5,7) for triangle one. The x side is labeld a and the angle near the origin is alpha. Now the second triangle is against the y side or against the side from (5,0)