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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

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..

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

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

Equilateral 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

Right Triangle Functions

Please give answer and explanation and or steps if needed please to check my work. 1) Draw a right triangle whose sides (not the hypotenuse) have lengths of 8 and 15. Angle A is adjacent to the side of 8, and angle B is adjacent to the side with the length of 15. The tan A=? 2) For the same triangle in question 1 do f

Perimeter of a Triangle

The length of the sides of a triangle are 1/x, 1/2x, and 2/3x meters. Find a rational expression for the perimeter of the triangle (your final expression must contain only one term). Use Appendix A of Dugopolski for formulas of Geometric shapes. (Question also in attachment).

Geometry Construction- To Construct A Congruent Triangle

Step 1. Draw an acute scalene triangle. Label the vertices A, B,C on the interior of each angle. Step 2. Construct a segment congruent to line segment AC. Label the endpoints D and E. Step3. Adjust the compass setting to the length of line segment AB. Place the compass at point D and draw a large arc above line segment D

Area of quadrilateral

The perimeter of a building is 74'by 59'by 103'by 121'. How can the square footage of the building be calculated?

Triangle angles

Given triangle ABC with no angle >120 degrees, find and construct the point P for which PA + PB + PC is a minimum. What is this point called? What would be the case for a triangle with an angle of 120 degrees or more?

Two triangles: The lengths of the sides opposite the angles.

In this question ABC and PQR are two triangles, and the lengths of the sides opposite the angles A,B,C P, Q, R are a,b,c,p,q,r, respectively. Choose the THREE false statements. Options. A. If angle A= angle Q and angle B= angle P. then it must follow that c b --- = -- r p B. I

The Radius of the Circumscribed circle for a triangle

The circumscribed circle is the circle passing through the three vertices of a triangle ABC. Assume the following results from geometry. The perpendicular bisectors of the sides of a triangle meet in a point O that is the center of the circumscribed circle. a) According to a theorem from geometry, the measure of the angle

Geometric proof

Prove that the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices.

Right triangles

How do I find the third angle in a right angle triangle if I know one of the angle's is 65 deg?