Numerade

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Find the lengths of the following curves.\ a. $y = -\frac{x^2}{8} + \ln x$, $2 \le x \le 12$\ b. $x = \left(\frac{y}{7}\right)^2 - \frac{49}{8}\ln\left(\frac{y}{7}\right)$, $3 \le y \le 6$\ a. The length of the curve is $\frac{35}{2} + \ln(6)$.\ (Type an exact answer.)\ b. The length of the curve is $?$.\ (Type an exact answer.)

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The figure above shows a stick (long slender rod) of length L=1.85m and mass 0.35kg that oscillates as a physical pendulum about an axis shown at point O. Assume the oscillation is free from friction, air resistance, etc. (a) Derive an expression for the rotational inertia of the rod if it is free to rotate about the axis marked at O. (b) Calculate the period of the physical pendulum if the value x is 0.2m. (c) Determine the least period that this physical pendulum may oscillate by producing a computer-generated plot of the period, T versus the distance, x. Vary the distance x from (L)/(2) meters (the pivot is at the end of the rod) to zero meters (the pivot is at the center of the rod) You may use computer-based methods for finding the minimum period from the plot or you may also use the calculus method and setting the derivative equal to zero and solving for T_(min). (d) At what value for x will the least period be achieved? (e) How will this result for minimum period change if the mass of the rod is 10 times as much as the original mass? Explain why. L/2 The figure above shows a stick (long slender rod) of length L = 1.85 m and mass 0.35 kg that oscillates as a physical pendulum about an axis shown at point O. Assume the oscillation is free from friction, air resistance, etc. (a) Derive an expression for the rotational inertia of the rod if it is free to rotate about the axis marked at O. (b) Calculate the period of the physical pendulum if the value x is 0.2 m. (c) Determine the least period that this physical pendulum may oscillate by producing a computer-generated plot of the period, T versus the distance, x. Vary the distance x from L/2 meters (the pivot is at the end of the rod) to zero meters (the pivot is at the center of the rod)You may use computer-based methods for finding the minimum period from the plot or you may also use the calculus method and setting the derivative equal to zero and solving for Tmin- (d) At what value for x will the least period be achieved? (e) How will this result for minimum period change if the mass of the rod is 10 times as much as the original mass? Explain why.

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24) If $f(x) = 4\sqrt[3]{x} + x$ use the line tangent to f at (8,16) to approximate f(27).

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$1$ point) Find $\frac{dy}{dx}$ by implicit differentiation, where $9x^5 + x^2y^5 + 6y^4 = 9$. \n$\frac{dy}{dx} = $

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28. Given the following code: 1 1 (function(window) { 2 2 3 3 var obj = {}; 4 4 5 5 obj.dreamon = function () { 6 6 console.log("I want to see the global scope! Let me out!"); 7 7}; 8 8 9 9 window.doer = obj; 10 10 11 11 }); 12 12 13 13 doer.dreamon(); What (if anything) is missing from this code in order to get it to output the message of the "dreamOn" method? 4 Marks A. Nothing is missing. It will output "I want to see the global scope! Let me out!" B. Line 1 and Line 9 should use 'global' instead of 'window'. C. The function definition in Line 5 is missing an argument. It should accept an argument by the name of 'window' D. The attempted IIFE is not being invoked and passed in the window object. It's missing '(window)' Line 11 right before the semicolon. 29. In style sheets, more than one rule can be assigned to a particular element, but the browser will follow only the rule that takes precedence. A. True B. False 30. Is JavaScript and ECMAScript are same? Explain if not.

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Average service time (hours): 0.75 Required Service Time (hours) Probabililty 0.1 0.6958 0.2 0.6455 0.3 0.5989 0.4 0.5556 0.5 0.5155 0.6 0.4782 0.7 0.4437 0.8 0.4116 0.9 0.3819 1 0.3543 1.1 0.3287 1.2 0.3049 1.3 0.2829 1.4 0.2625 1.5 0.2435 1.6 0.2259 1.7 0.2096 1.8 0.1944 1.9 0.1804 2 0.1673 2.1 0.1553 2.2 0.1440 2.3 0.1336 2.4 0.1240 2.5 0.1150 2.6 0.1067 2.7 0.0990 2.8 0.0918 2.9 0.0852 3 0.0790 3.1 0.0733 3.2 0.0680 3.3 0.0631 3.4 0.0586 3.5 0.0543 3.6 0.0504 3.7 0.0468 3.8 0.0434 3.9 0.0402 4 0.0373 What is the probability that a ring will take 60 minutes to service? 0.3543 What is the probability that a ring will take 30 minutes or less to service? 0.3127 What is the probability that a ring will take more than 30 and less than or equal to 60 minutes to service? What is the probability that a ring will take more than 90 minutes or longer to service? Exponential Distribution 0.8000 0.7000 0.6000 0.5000 0.4000 0.3000 0.2000 0.1000 0.0000 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

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Calculate Rt for the circuit in the below figure. Note that R1 = 1.4 kOhm and R2 = 2.2 kOhm. R1 R2 W The result should be in Ohm Calculate Answers to 2 decimal points

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Peaks and troughs (highs and lows) is a description of... Pro forma mapping Using media flighting Scalability ROI (return on investment)

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b. Oxygen; Carbon Dioxide d. Carbon Dioxide; Hydrogen 20. Which chamber initially receives blood from the systemic circuit? a. Left atrium b. Left ventricle c. Right atrium d. Right ventricle 21. Coronary bypass surgery a. Removes excess adipose tissue in areas where those cells are unwanted b. Uses a machine to filter toxins from the blood c. Places a tubular support with mesh wiring in the inside of a blood vessel to relieve an obstruction d. Redirects blood around a section of a blocked or partially blocked artery in your heart by taking a healthy blood vessel from another part of your body and connecting it beyond the blocked arteries in your heart

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Based on the graph below, answer the following question. (A) (B) [Cell concentration] [Time] In a test tube, you have two bacteria. Suspecting one uses aerobic respiration and the other uses anaerobic chemolithotrophy, you provide the following in a test tube containing both bacteria: oxygen, glucose, Fe as an electron donor, and a mixture of macronutrients and micronutrients. Predict which curve likely reflects the aerobic respiring bacterium and which curve likely reflects the bacterium using anaerobic chemilothotrophy over time. • (Part i; 2 pts) State which curve is the aerobic respiring bacterium, and which curve is the bacterium using anaerobic chemolithotrophy. • (Part ii; 4 pts) Explain why the curves look the way they do, e.g., why does curve A decrease with time and curve B increase with time.

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joaquin f.