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Geometry

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

Pascal's Triangle Representation

(See attached file for full problem description) --- The question is =========== Let S_(n,0), S_(n,1), and S_(n,2) represent the sums of every third element in the nth row of Pascal's Triangle beginning on the left. For example: Row 5: 1 5 10 10 5 1 So, S_(5,0) = 1 + 10 = 11 S_(5,1) = 5 + 5 = 10 S_(5,2) =

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

Functions and Graphs (4) Problems

(See attached file for full problem description with diagrams) --- (1) A Little League team is building a backstop for its practice field. It is made up of two right angles as shown below. The backstop extends 24 feet 8 inches out in each direction and the center pole is 6.5 yards high. All sides of the backstop including ba

Area, Volume and Worker Efficiency

1. Volume of a container. A cubic shipping container had a volume of 3 cubic meters. The height was decreased by a whole number of meters and the width was increased by a whole number of meters so that the volume of the container is now a3+2a2- 3a cubic meters. By how many meters were the height and width changed? 2. Worker e

Coordinate Geometry : Triangles and Lines through Triangles

The points A(-1, -2), B(7, 2) and C(k, 4), where k is a constant are the vertices of traingle ABC. Angle ABC is a right angle. 1. Calculate the value of k 2. Find the exact area of traiangle ABC 3. Find the equqtion for the stright line l passing therough B and C. Give your answer in the form of ax + by = c = 0 , where a, b

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

A. Find an equation of a straight 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.

Height and Distance: Similar triangles.

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.

Several Geometry problems

(See attached file for full problem description and diagrams) --- 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

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

Geometry and everyday life

Questions (also attached): A Little League team is building a backstop for its practice field. It is made up of two right angles as shown below. The backstop extends 24 feet 8 inches out in each direction and the center pole is 6.5 yards high. All sides of the backstop including base and the center pole are to be made o

A practical application of geometry: Right Angles

A Little League team is building a backstop for its practice field. It is made up of two right angles as shown below. The backstop extends 24 feet 8 inches out in each direction and the center pole is 6.5 yards high. All sides of the backstop including base and the center pole are to be made of aluminum tubing. How many feet of

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 and Sum of Measures of Acute Angles

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 problem..

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.

Geometry Proof: Isoceles Triangle

1.Given: B is the midpoint of AC BD is perpendicular to AC Prove Triangle ADC is isosceles (hint: first prove triangle CBD is congruent to triangle ABD) The second part uses to same diagram Given DB is perp to AC AD is congruent to DC m of angle C is 70 degrees Find measure of ADB

Determining Area

I am trying to determine the area of a triangular item that has an area of x2 + 5x + 6 (the 2 is squared) square meters and a height of x + 3 meters. I am trying to determine the length of the base.

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.