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Triangles

Find the area covered by the chemical retardant.

1) In mountain communities, helicopters drop chemical retardants over areas which approximate the shape of an isosceles triangle having a vertex angle of 38 degrees. The angle is included by two sides, each measuring 20 ft. Find the area covered by the chemical retardant. 2) The chemical retardants are freight shipped from

Solving Radical Equations and Finding Side of a Cube Given Volume

1) Solve the following equations. a) sqrt(x) - 1 = 4 b) sqrt(x^3) = 8 c) third root of x^2 = 4 2) Is sqrt(x^2) an identity (true for all values of x)? Answer: Explain your answer in this space. 3) For the equation x - sqrt(x) = 0, perform the following: a) Solve for all values of x that satisfies the equatio

Geometry Proofs : Triangles, Bisectors and Midpoints

1- Given triangle as shown (infigure 241W) with AF = 1/4 AB, AE = 1/3 and BE Intersect CF = O (BE has ray bar on top and CF has distance bar on top) prove that AO hits BC At its midpoint. 2- Use Ceva's theorem to prove that the internal bisectors of the angles of a triangle are concurrent (cevas theorem: given triangle AB

Internal bisectors and incenter of a triangle

1- Given triangle ABC, prove that an internal bisectors of an angle of a triangle divides the opposite sides (internally) into two segments proportional to the adjacent sides of the triangle. That is prove that DB/DC = AB/AC. (D is the point where e internal bisector of <A meets with BC) 2- Given triangle ABC with in-center

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

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

Triangles

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

Rectangle

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)

Right triangles

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