Prove that on the side of a regular hexagon and outside the hexagon we construct six...

Prove that on the side of a regular hexagon and outside the hexagon we construct six squares. the exterior vertices of these squares are those of a regular dodecagon

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The base of a right pyramid is a regular hexagon with sides of length 10 m....

The base of a right pyramid is a regular hexagon with sides of length 10 m. The altitude is 5 m. Find the total surface area of the pyramid. The area is _______m2.

Using Euclid's Propositions: 1. Prove that the regular octagon is constructible. 2. Prove that the regular...

Using Euclid's Propositions: 1. Prove that the regular octagon is constructible. 2. Prove that the regular decagon is constructible.

prove Pascal's mystic hexagon theorem and Brianchon's theorem which is the dual to Pascal's

A soccer ball has 32 faces, each of which is a regular pentagon or hexagon. Because...

A soccer ball has 32 faces, each of which is a regular pentagon or hexagon. Because of the angles involved, exactly three faces meet at each corner. Without looking at the ball, determine how many of each type of face there are.

Prove that two quadrilaterals are congruent if a side, angle, side, angle, side of one are...

Prove that two quadrilaterals are congruent if a side, angle, side, angle, side of one are equal to the corresponding parts of the other, the five parts in each case being consecutive on the quadrilateral. (can you find a counter example if the quadrilaterals are not convex?)

In all parts of this problem, assume that we are using fair, regular dice (six-sided with...

In all parts of this problem, assume that we are using fair, regular dice (six-sided with values 1, 2, 3, 4, 5, 6 appearing equally likely). Furthermore, assume that all dice rolls are mutually independent events. (a) [4 pts] You roll two dice and look at the sum of the faces that come up. What is the expected value of this sum? Express your answer as a real number. (b) [7 pts] Assuming that the two dice are independent, calculate...

Prove whether the following are regular (include the file) or not regular (attach a proof). The...

Prove whether the following are regular (include the file) or not regular (attach a proof). The alphabet is {0, 1}. 1. The set of strings that start with N 0's which are directly followed by 2N 1's. 2. The set of strings start with two 0's, followed by N 1's, followed by N 1's and end with three 0's. 3. The set of strings where every substring of length 5 has more 0's than 1's. Strings less than length five...

(EXCEL) Create a user-defined function called Hexagon that takes one argument called side and returns the...

(EXCEL) Create a user-defined function called Hexagon that takes one argument called side and returns the area of a regular hexagon given the length of the side. Show that the function works in a worksheet by inserting the formula somewhere.

Consider the following figure. A hexagon has six labeled vertices and a dashed line segment which...

Consider the following figure. A hexagon has six labeled vertices and a dashed line segment which divides the hexagon into a trapezoid and rectangle. The first side is horizontal, starts at vertex R, goes to the right, and ends at vertex S. The second side is vertical, starts at vertex S, goes up, and ends at vertex T. The third side starts at vertex T, goes up and to the right, and ends at vertex V. The fourth side is...

Are the following languages over {a, b} regular? If they are then prove it. If they...

Are the following languages over {a, b} regular? If they are then prove it. If they are not prove it with the Pumping Lemma a) {ap | p is a prime number} b) {xax | x Î{a,b}*} (start by listing some strings in, not in, the language

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