Numerade

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Question 1 1.1 Briefly discuss the three stages in the development of algebra. (6) 1.2 Describe the aims of algebra. Also, provide examples of each of the aims described. (18) 1.3 Describe the stages in the development of symbolic algebra. Give at least one example of an equation for each of the stages. (6) 1.4 Discuss cultural artifacts (African and non-African) that may be interpreted (described) algebraically. Also, give the names of the countries of origin where these artifacts are found. (10) 1.5 With the aid of at least one example, describe each of the following concepts: 1.5.1 Mathematics expression and (2) 1.5.2 Mathematics equation. (2) 1.6 Differentiate between the following concepts: a numerical expression, an arithmetic expression, an algebraic expression, and an equation. (6) 1.7 Name four different representations of mathematical ideas in the learning of algebra. (4)

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identify the relationship between experimental treatment, conspecific density, and plant fitness that demonstrates the excluded pest causes negative density dependence.

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Which of the following principles requires that World Trade Organization (WTO) member states treat like goods coming from other WTO member states on an equal basis?

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7) [18pt] Suppose $f(x) = \sqrt{x}$. a) Find the second order Taylor polynomial, $p_2(x)$, for $f(x) = \sqrt{x}$ centered at $a = 1$. b) Use $p_2$ from part (a) to approximate $\sqrt{2}$. c) Using Taylor's Theorem, find a bound for the error in the approximation in part (b).

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8. The most important battery technology in the near future is the lithium-ion batteries. Lithium ion batteries show the most promise for developing electric cars. Please review the notes on lithium-ion batteries and please do a brief google search on lithium-ion battery chemistry. a. Make a nice hand-drawn sketch of a lithium-ion battery similar to the figure in the notes. b. Write a short paragraph explaining the chemistry on the positive plates. c. Write a short paragraph explaining the chemistry on the negative plates. d. Write a short paragraph explaining how the electrolyte works.

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1. Three charges, +q, +q, and -q, are distributed at equal intervals around a circle as shown in the diagram below. +q No zero field +q \vec{F}_{net} force with pencil Fast +q X (2q70) slow A 3 (a) Draw the direction of the field at each of points A, B, C, D. Label point(s) (if any) where the field is zero in the plane of the paper with an X. missing two X 3 (b) Rank the strength of the field at each of points A, B, C, D. (c) Draw the direction of the net force on each of the charges. weakest B>D>A>C B> (C?D) >A (d) Draw two possible paths an electron ($|q| >> |e|$) could take if it were incident on the center of the circle from the left, with either \"fast\" or \"slow\" initial velocity (label accordingly).

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Find the tension in the cable. 125 mm 175 mm A B C D 225 mm 150 N 75 mm

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Consider a second-price auction with 2 players. Player 1 values the object at $10, and Player 2 values it at $6. Each simultaneously submits a bid for the object; the highest bidder wins, and pays the amount of the loser's bid. Loser pays nothing. Which of the following are is/are NE, assuming that P1 wins in a tie: (a) P1 bids 10, P2 bids 10. (b) P1 bids 10, P2 bids 0. (c) P1 bids 0, P2 bids 10. (d) Two of these (e) Three of these

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z = 0 P_{tank} = 200 kPa z = 40 m Nozzle diameter 3.0 cm gravity 30° V_{jet} M_{cart} = 100 kg 5 m

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A large refracting telescope has an objective lens with a focal length of 10 m. what angular magnification does it produce when a 2.90 m focal length eyepiece is used?

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jonathan s.