The cost C(x) of the pipeline as a function of x is: C(x) = distance along north shore * pipeline cost over land + distance under the river * pipeline cost under land The distance along the north shore is 6-x The distance (by Pythagorean theorem) under the water is sqrt( 2^2 + x^2) So‚ C(x) = (6-x)*200000 + sqrt(4 + x^2) * 400000 [You should graph this] To find the value of x where C(x) is minimized‚ we set dC/dx = 0‚ [Reminder - use the chain rule to differentiate the second term]
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With the help of tape measures and rules small distances in the everyday household are easy to measure. As distances grow bigger so do the devices and ways in which the distance is to be measured. In math rulers make sense as well as Pythagorean Theorem; so what about astronomy? Astronomers have a totally different format of information of which they are studying. It only makes sense that the astronomers would have a totally different way of which they measure. Two measurements astronomers use are
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are numbers. Mathematics is the basis for everything‚ and geometry is the highest form of mathematical studies. The physical world can understood through mathematics” Pythagoras is probably best known for his discovery of the Pythagorean Theorem. Not only did the group practice mathematics and religious topics‚ but they also became involved with the politics in Croton. Their involvement in the politics of Croton was not taken too kindly. The people of Croton burned down some of the meeting
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between any horizontal lines is the difference between the absolute value of x1 and x2 or vice versus. Distance Formula Activities III: Students will find the distance between 2 points using the distance formula and the Pythagorean Theorem will also be reviewed. Students should be able to find the distance between 2 points on a coordinate plane after these activities.
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was that the health of all living creatures depended on a proper balance of elements and if the balance was not right the person or animal was unhealthy (The Basics of Philosophy"‚ 2008). Pythagoras was also credited for creating the Pythagorean Theorem‚ a geometrical theory that we recognized as A2 + B2 = C2. This theory states that the hypotenuse of a right triangle is equal to the square of the other sides. Pythagoras also believed that he had lived previous lives and that all creatures were
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numbers that could be delivered. __T__ 6. When assigning subjective probabilities‚ use experience‚ intuition‚ and any available data. __F__ 7. P (AxB) d P (A) __F__ 8. If P (A|B) = .4 and P (B) = .6‚ then P (AxB) = .667. __T__ 9. Bayes’ theorem provides a way to transform prior probabilities into posterior probabilities. __T__ 10. If P (AyB) = P (A) + P (B)‚ then A and B are mutually exclusive. Section B Multiple Choice Identify the letter of the choice that best completes the statement
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While both the Egyptian and Babylonian time periods certainly influenced future mathematics‚ it seems to be Babylon that had the most to offer. Egypt achieved many feats that required skill in mathematics‚ but it isn’t completely clear how they came about these as their use of papyrus meant much information did not survive. This doesn’t mean that they didn’t influence the societies and people that came after or from them. It is simply that because of the limited information about their mathematic
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P(Unsuccessful venture | Unfav survey) = 0.6 Iverstine & Walker Probabilities P(Fav survey | Succes) = 0.9 P(Unfav survey | Success) = 0.1 P(Fav survey | Failure) = 0.2 P(Unfav survey | Failure) = 0.8 Calculations for Posterior Probabilities (Bayes Theorem) included in decision tree Posterior Probabilities for Iverstine & Walker if Survey is Favorable Outcome P(Fav survey | Outcome) Prior Probability Join Prob Posterior Joint Prob Equation Posterior Prob Equation
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As students‚ we are taught the basics about mathematics. What the core properties of addition‚ subtraction‚ multiplication and division mean. How they work‚ and if we are lucky‚ we go into a little history of these methods. For those of us who have learned history‚ we learned that the basis for modern mathematics came from the Greeks and their writings. While this is correct‚ to truly understand the historical aspect of mathematics and its origins‚ one must study a time before the Greeks‚ when math
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formed the basic element of science. From this basic element came the luxuries we enjoy today. Pythagoras‚ a mathematician‚ proved "the relationship between the legs and the hypotenuse of a right triangle."1 From this‚ he derived the Pythagorean Theorem. This contribution mainly influenced architecture and geometry today. Equally‚ Eratosthenes also influenced architecture and geometry. He developed a method of determining the circumference of the Earth by using geometry. Developed by Archimedes‚
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