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Value of Theta: Maximum Area of Triangle

An isosceles triangle has two equal sides of length 10cm. Let theta be the angle between the two equal sides. The Area of the triangle can be expressed as: A(theta) = 50sin(theta) If theta is increasing at the rate of 10 degrees per minute (pie/18 radians per minute)and the derivative of the area is [50cos(theta)]at what valu

Equilateral Triangle Problem

Let's say you hgave an area with 100 feet of fence. Two configurations were a circle and a rectangle. What other possibilities of utilizing other shapes for this fenced in area. Could you create a figure with a larger area than the circle? In particular an equilateral triangle: A=(1/4) (s 2nd power) (3 1/2 power)where S is th

Centroid theorem proof and deriving the distance formula

Prove the CENTROID therorem using the VECTOR proof as well as the SYNTHETIC proof Explain how to derive the distance formula (assuming that the distance formula is not yet known), first in 2 dimentional and then in 3 dimentional

Geometry problems

What is a polygon? What is the difference between an equiangular polygon, an equilateral polygon, and a regular polygon? Provide an example of each. We can use the Pythagorean theorem to solve problems that involve right triangles. Provide an example of a day-to-day situation that involves right triangles and the use of th

Geometry Problems

Please correct and explain. 1. Are the angles of a triangle considered to be supplementary? _Yes Explain your answer. Any two angles that add up to 180 degrees are known as supplementary angles. Three angles inside any triangle always add up to 180 degrees. Classify the following as true or false. If false, tell why

Geometry in Real-Life

For geometry I am having trouble to come up with an example for the question below that illustrate numbers. I need an example with numbers and some geometry calculations so that we can clearly see how geometry is used in our everyday life?

Strategies for Teaching the Solving of Math Problems

Describe a general process that students in grades 5-8 or 9-12 can use to solve problems. B. Describe at least five specific problem-solving strategies that these students can use to solve mathematics problems. For each strategy, give an example. C. Discuss how these strategies and processes encourage students to persist

Metric Space Proofs

Problem 1: Given the metric space (X, p), prove that a) |p(x, z) - p(y, u)| < p(x, y) + p(z, u) (x, y, z, u is an element of X); b) |p(x, y) - p(y, z)| < p(x, y) (x, y, z is an element of X). These problems are from Metric Space. Please give formal proofs for both (a) and (b) based on the reference provided. Thank y

Word Problem Involving Tangent Function

A patient is being treated with laser therapy to remove a tumour that is located behind a vital organ. The tumor is 5.7 cm below the skin. To avoid the organ, the entry point of the laser must be 12.4 cm above the tumour along the skin. What is the angle the doctor must use to hit the tumor directly? Round your anwer to the near

Mathematics - Geometry - Pythogorean Theorem

1) A right triangle is a triangle with one angle measuring 90^o. In a right triangle, the sides are related by Pythagorean Theorem, , where c is the hypotenuse (the side opposite the 90^o angle). Find the hypotenuse when the other 2 sides' measurements are 6 feet and 8 feet. 2)Suppose you travel north for 65 kilometers then t

Geometry : Polygons and Geoboards

26. On a sheet of dot paper or on a geoboard like the one shown, create the following: a. Right angle b. Acute angle c. Obtuse angle 1. Adjacent angles e. Parallel segments 1. lntersecting segments Draw three different nonconvex polygons. When you walk around a polygon, at each vertex you need to turn either right (cloc

Congruent and similar triangles

See attachment A. Find at least three examples of congruent objects in a typical classroom. (don't need pictures). What out of class activities could you employ to make students aware of congruent objects? Stan is standing on the bank of a river wearing a baseball cap. Standing erect and looking directly at th

Real life examples of various types of triangles and graph

See attachment. Below is a list of various types of triangles: 1) Right triangle 2) Acute triangle 3) Obtuse triangle 4) Scalene triangle 5) Isosceles triangle 6) Equilateral triangle find an example of each of these triangles in your daily life. For example, Yield signs are a good example of acute

Find the symmetries of the regular tessellations in a plane

Square- we are to explain reflection: how many lines( 2 edges, 2 bisectors, vertex arrangement is order is 4 90degrees, rotation :center of shape is order 4, midpoint is order 2 180. triangle- reflection 6lines(3edges and 3 bisectors), vertex arrangement is very similar to hexagon but(please explain) order 6 (60 degrees)

Important Information About Tessellations

Please help write a formula, explained mathematically and show work. Show a drawing showing they repeat. Show examples of all 8 and go into detail please. Find (and describe) all the regular tessellations of the plane. Note that septagons, nonagons, and 11-gons are not provided. How do you know each one you find really fills

relationship among three sides of a triangle

Please give a thorough explanation. Thanks. 1.Is it possible to have a triangle with sides measuring 10ft, 12 ft, and 23 ft.? 2.A mountain road is inclined 30 degrees with the horizontal, if a pick-up truck drives 2 mi. on this road , what change in altitude has been achieved?

Explanation of how two isosceles triangles are similar.

Please give a through explanation to the following. thank you Answer true or false. a. If each of two isosceles triangles has an angle that measures 120 degrees, then the two isosceles triangles must be similiar. b. If each of two isosceles triangles has an angle that measures 40 degrees, then the two isosceles triangles m

Prove triangle ABC is congruent to triangle DBE.

1. Write a proof. AB*BE = CB*BD. Prove triangle ABC is congruent to triangle DBE. 2. A parent group wants to double the area of a playground. The measurements of the playground are width is 2W and the length is 2L. They ask you to comment. What would you say? 3. Find the length of the altitude drawn to the hypotenuse.

Geometry Theorem Proof

Prove that an interior angle bisector of any triangle divides the side of the triangle opposite the angle into segments proportional to the adjacent sides.

Geometry - Parallelograms and Triangles

Please solve. See the attached file for diagrams. Question 1 The preferred seating area at the Music Theatre is the shape of a parallelogram. Its base is 34 yd and its height is 39.6 yd. Find the area. Question 2 The diagonal of a small pasture measures square root 12,617 feet in length. Find the le

Oblique Triangles and Identities

A) Verify the following Identities : i) [(Sin 2theta)/ (sin theta )- ( cos 2theta/ cos theta )] = sec theta ii) cos2x = (cot^2 x-1 )/ (cot^2 x-1 ) And, ììì) Use logarithms and the law of tangents to solve the triangle ABC, given that a= 21.46 ft, b= 46.28 ft, and C = 32° 28' 30

Area of Oblique Triangles

A) Find the area of the isosceles triangle in which each of the equal sides is 14.72 in and the vertex angle is 47° 28' . B) Find the radius of the inscribed circle and the radius of the circumscribed circle for the following obliqe triangle : a) = 12.7 , b = 21.5, and c = 28.6

The Volume of a Tetrahedron

Computing the Volume of a regular tetrahedron of edge length 2(alpha). Explain how to compute the volume of a regular tetrahedron of edge length 2(alpha).

Find the volume of a tetrahedron and an octahedron.

I need help writing a proof of the formulas of the volumes of two regular polyhedra (Platonic solids): (1) a tetrahedron and (2) an octahedron. I then have to use those formulas to find the volumes given a side length of 1.