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Find the arc-length of C1 and C2. Use this information to show that both bugs reach the origin at the same time To and find the exact value of To.
A telephone pole 35ft. tall has a guy wire attached to it 5 ft. from the top and tied to a ring on the ground 15 feet from the base of the pole.
Prove the the center of gravity of a lamina in the shape of a parallelogram is at the point of intersection of the diagonals.
The height of the house shown here can be found by comparing its shadow to the shadow cast by a 3-foot stick.
Transform each equation to standard form. Then find the center, foci, major and minor axes, and ends of each latus rectum. Draw the curve
How many squares on the checkered flag contain an equal number of white and black squares? Be sure to describe how you arrived at your answer.
The length of a rectangular floor is 8 meter less than twice its width. If a diagonal of the rectangle is20 meters, find the length and width of the floor.
If C6 acts on a regular hexagon by rotation and each of the vertices is colored red, blue or green, use the Burnside's formula.
Show how you can find the length of each side, the angles and area of the hexagon and please show the diagram.
What is the relationship between the volumes of the two figures? Explain in words using an example.
Given a right triangle with legs a and b, and hypotenuse c, find the missing side. A=9, b+12
Prove that the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices.
The circumscribed circle is the circle passing through the three vertices of a triangle ABC. Assume the following results from geometry.
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?
If A,B,C are noncollinear in a metric geometry prove that triangle ABC is convex.
The perimeter of a building is 74'by 59'by 103'by 121'. How can the square footage of the building be calculated?
Draw an acute scalene triangle. Label the vertices A, B,C on the interior of each angle.
Given triangle ABC, prove that an internal bisectors of an angle of a triangle divides the opposite sides (internally).
Geometry has many practical applications in everyday life. Estimating heights of objects, finding distances, and calculating areas and volumes are common place.
Show how to construct a triangle given the length of one side, the distance from an adjacent vertex to the incenter and the radius of the incircle.
A wire 10 meters long is to be cut into two pieces. One piece will be shaped as an equilateral triangle, and the other piece will be shaped as a circle.
Prove the first half of the open-jaw inequality where the point G lies inside triangle DEF i.e. show that if x less than y => AC < DF.
Let (triangle DEF) be equilateral triangle and Q is a point inside. Prove that the sum of the three distances from Q to each side is equal to the altitude DD'.
A surveyor finds that a tree on the opposite bank of a river has a bearing of N 22 degrees 30'E from a certain point and a bearing of N 15 degrees.
Show the necessary steps for finding the length of each side of a regular hexagon if opposite sides from midpoint to midpoint are 18 inches apart.