(a) The table shows some of the possible dimensions of the rectangle. Find the values of a‚ b‚ c‚ d and e. Length (m) Width (m) Area (m2) 1 11 11 a 10 b 3 c 27 4 d e (2) 3 (b) If the length of the rectangle is x m‚ and the area is A m2‚ express A in terms of x only. (1) (c) What are the length and width of the rectangle if the area is to be a maximum? (3) (Total 6 marks) 5. (a) Solve the equation x2 – 5x + 6 = 0. (b) Find the coordinates of the points where the graph of y
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Logarithmic Equations Exponential Equations (variable in exponent position) 1. Isolate the exponential portion ( base exp onent ): Move all non-exponential factors or terms to the other side of the equation. 2. Take ln or log of each side of the equation. • Make sure to use ln if the base is “e”. Then remember that ln e = 1 . • Make sure to use log if the base is 10. • If the base is neither “e” nor “10”‚ use either ln or log‚ your choice.. 3. Bring the power (exponent) down into coefficient position
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1.) What does the pilot want? To save the girl. 2.) Is the pilot likely to succeed? Most likely not because by doing so he would kill others. 3.)What does the sister want? She wants to live. 4.) Is the sister likely to succeed? I doubt it cause of there being a law and there seems theers no other way then her diying. 5.) What does the government want? For the girl to be thrown off the ship. 6.) Is the government likely to succeed? I belive so. 7.) What should happen? The girl should be saved
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Scranton Engineers Club. This formula is given as Where σp is pillar strength‚ σ1 is uniaxial compressive strength of a cubical specimen (w/h = 1)‚ and w and h are pillar dimensions. According to Obert and Duvall‚ this equation is valid for w/h ratios of 0.25 to 4.0‚ assuming gravity-loading conditions. Through back calculations from mining case histories and utilization of laboratory rock properties‚ safety factors of 2 to 4 were derived for short- and long-term pillar
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using an average variable cost function of the form. AVC= a + bQ+ cQ^2 (the 2 is suppose to be exponent) Where AVC=dollars per vacuum cleaner and Q=number of vacuum cleaners produced each month. Total fixed cost each month is $180‚000. The following results were obtained: Dependent Variable:AVC R-Square F-Ratio P-Value on F Observations:19 0.7360 39.428 0.0001 Variable
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------------------------------------------------- Equations and Problem-Solving * An airplane accelerates down a runway at 3.20 m/s2 for 32.8 s until is finally lifts off the ground. Determine the distance travelled before take-off. ------------------------------------------------- Solutions Given: a = +3.2 m/s2 | t = 32.8 s | vi = 0 m/s | | Find:d = ?? | d = VI*t + 0.5*a*t2 d = (0 m/s)*(32.8 s) + 0.5*(3.20 m/s2)*(32.8 s)2 d = 1720 m ------------------------------------------------- Equations and Problem-Solving
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Date Performed: January 10 & 15‚ 2013 Spectrophotometric Determination of the Equilibrium Constant of a Reaction R.J.V. Ortega and J.C.V. Gatdula Institute of Chemistry‚ College of Science University of the Philippines‚ Diliman‚ Quezon City‚ Philippines Received January 22‚ 2013 ------------------------------------------------- ------------------------------------------------- ------------------------------------------------- ABSTRACT -------------------------------------------------
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Without knowing something about differential equations and methods of solving them‚ it is difficult to appreciate the history of this important branch of mathematics. Further‚ the development of differential equations is intimately interwoven with the general development of mathematics and cannot be separated from it. Nevertheless‚ to provide some historical perspective‚ we indicate here some of the major trends in the history of the subject‚ and identify the most prominent early contributors. Other
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2-Variable Inequality Here is an example of a problem very similar to the one in the Week Three Assignment: Catskills Hammock Company can obtain at most 2000 yards of striped canvas for making its full size and chair size hammocks. A full size hammock requires 10 yards of canvas and the chair size requires 5 yards of canvas. Write an inequality that limits the number of striped hammocks of each type which can be made. (b) First I must define what variables I will be using in my inequality
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Some say that the idea of love in modern terms differs conceptually from that of earlier periods. That argument is demonstrably false. Although love has been characterized in many different ways throughout the ages‚ the fundamental idea remains constant. No matter the eccentric personalities love is entitled to‚ love is what it is. From a literary point of view‚ whether one reads the tender longing of Sappho‚ the unattainable desire of Petrarch‚ or the whimsical prose of Dickenson‚ the message
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