Treasure Hunt: Finding the Values of Right Angle Triangles This final weeks course asks us to find a treasure with two pieces of a map. Now this may not be a common use of the Pythagorean Theorem to solve the distances for a right angled triangle but it is a fun exercise to find the values of the right angle triangle. Buried treasure: Ahmed has half of a treasure map‚which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map
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Immanuel Kant and Blaise Pascal offer contrasting opinions concerning reason‚ or man’s ability to come to conclusions on his own. In Metaphysics of Morals‚ Kant provides an optimistic view of reason‚ depicting that reason can attain certain conclusions. Pascal argues in Pensees that man is inherently flawed and can’t be certain from reasoning while faith‚ or belief in the supernatural‚ is the only thing that can create certainty. Kant’s positive outlook on human reason is a sound assertion‚ although
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Ex: This process can be even easier. Blaise Pascal‚ a famous French mathematical among other things put together a triangle made up of numbers where each number represents the coefficient of each term (when expanded) in a binomial to a certain power. He named the triangle “triangle du arithmétique” or in English‚ “The Arithmetical Triangle”. Now the triangle is called “Pascal’s triangle named after the creator‚ Blaise Pascal. We can find this triangle by using combinations. Ex: Moving back to
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Does ‘Pascal’s Wager’ provide a convincing argument for belief in God? Published in 1670 and named after French philosopher and mathematician Blaise Pascal; the philosophical theory of Pascal’s Wager reasons that to believe in God is a decision made in a time of uncertainty. The Wager also explains that whether or not God exists‚ we can estimate the outcome; an infinite reward or an infinite punishment. This suggests that the rational choice to live as if God exists is the better of the possible
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the syllabus. (Marks 2)Question 13) In figure ABCD is a cyclic quadrilateral. AE is drawn parallel to CD and BA is produced. If ABC = 92o‚ FAE = 20o‚ find BCD. (Marks 2) No answer Question 14) Determine the length of an altitude of an equilateral triangle of side 2a cm. (Marks 2)Question 15) In the figure‚ a circle touches all the four sides of a quadrilateral ABCD where sides AB = 6 cm‚ BC = 7 cm and CD = 4 cm. Find AD. (Marks 2) sorry‚ no answer for this as I do not have diagram for this question>
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coefficients. They are the same as the entries of Pascal’s triangle‚ and can be determined by a simple formula involving factorials. These numbers also arise in combinatorics‚ where the coefficient of xn−kyk is equal to the number of different combinations of k elements that can be chosen from an n-element set. HISTORY : HISTORY This formula and the triangular arrangement of the binomial coefficients are often attributed to Blaise Pascal‚ who described them in the 17th century‚ but they were known
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Two triangles are said to be similar if every angle of one triangle has the same measure as the corresponding angle in the other triangle. The corresponding sides of similar triangles have lengths that are in the same proportion‚ and this property is also sufficient to establish similarity. A few basic theorems about similar triangles: * If two corresponding internal angles of two triangles have the same measure‚ the triangles are similar. * If two corresponding sides of two triangles are
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Vanessa will use her compass to find south side of the Castle Rock. Where she will walk “X” paces in a straight line south toward the Castle Rock and mark the place where a red flag is mark. At the end of her distance she will mark the red flag in a triangle. Vanessa will now turn 90 degrees to the right and will walk 2x+4 paces east until she tied rope at stick that marks the blue flag. We have now acquired a line segment which we will call Y for yellow flag and R for red flag and B for Blue flag
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Bermuda Triangle is an area in the Atlantic Ocean between Miami‚ Puerto Rico‚ and Bermuda. It has been nicknamed the Devil’s Triangle because it is known as a place in the ocean where planes and ships mysteriously disappear without providing an explanation. Over the years‚ many people have proposed a variety of theories in the hope of finding an explanation for all the unsolved mysteries that are held within the Bermuda Triangle. Many theories suggest that since the location of the triangle is subject
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MATH INVESTIGATION 4.2 FACTORIZATIONS on the Math Investigator determines if a number is prime or composite. If a number is composite‚ it prints all its factors‚ the number of factors‚ and its prime factorization. The numbers 1‚ 2‚ 4‚ and 6 have 1‚ 2‚ 3‚ and 4 factors‚ respectively: 1 has only 1 as a factor; 2 has 1 and 2 as factors; 4 has 1‚ 2‚ and 4 as factors; and 6 has 1‚ 2‚ 3‚ and 6 as factors. These factors are illustrated by the rectangles shown here. Starting Points for Investigations
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