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Describe how to find the arc length of a 60° arc with a radius of 3′-0" Add the result

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Required Information [The following information applies to the questions displayed below.] Permabilt Corporation was incorporated on January 1, 2022, and issued the following stock for cash: 2,000,000 shares of no-par common stock were authorized; 750,000 shares were issued on January 1, 2022, at $35 per share. 800,000 shares of $100 par value, 7.5% cumulative, preferred stock were authorized; 540,000 shares were issued on January 1, 2022, at $105 per share. No dividends were declared or paid during 2022 or 2023. However, on December 22, 2024, the board of directors of Permabilt Corporation declared dividends of $15,000,000, payable on February 12, 2025, to holders of record as of January 8, 2025. c. Calculate the common stock dividends per share declared during 2024. Note: Round your answer to 2 decimal places. Common stock dividends per share

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Consider the following reaction: 2 N$_2$H$_4$ (g) + N$_2$O$_4$ (g) $\rightarrow$ 4 H$_2$O (g) + 4 N$_2$ (g) If H$_2$O is produced at the rate of 3.47 M/s, what is the rate of production of N$_2$H$_4$? O a. 1.7 M/s O b. 4.6 M/s O c. 1.4 M/s O d. 6.9 M/s O e. 2.6 M/s

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1. Use the data set and the number of classes below to construct (a) an expanded frequency and relative frequency distribution table, (b) a frequency histogram, (c) a relative frequency histogram, (d) a frequency polygon, and (e) an ogive. 34 56 341 77 51 1 90 10 14 33 75 55 102 142 40 18 14 3 67 11 108 19 69 1 55 83 105 19 53 27 177 37 90 146 31 186 37 78 111 72 61 7 2 91 361 35 100 25 14 214 Number of classes: 8 (Round your answers to two decimal places if needed.)

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Determine if the function is a polynomial function. If it is, state its degree and leading coefficient a. f(x) = 5 - 8x - 9x^2

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5. Verify the polygon law for the shown balanced concurrent force system.

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2.9 Obtain the inverse Laplace transform $f(t)$ for the following: a. $\frac{5s}{s^2 + 9}$ c. $\frac{45}{s(s+3)^2}$ b. $\frac{6}{s^2 - 9}$ d. $\frac{2}{s(s^2 + 4s + 13)}$

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QUESTION 12 When the left abducens nerve is injured, which of the following eye muscles could be paralyzed and what movement of the left eye will be affected? Extrinsic Eye Muscles Superior oblique muscle Common Inferior Inferior tendinous rectus oblique ring muscle muscle Trochlea Trochlea Superior oblique tendon Superior Superior rectus oblique Superior rectus muscle, Lateral Medial rectus rectus -Lateral rectus muscle Inferior oblique Inferior rectus (a) Lateral view of the right eye 1. Superior oblique muscle. The left eye can't move downward and laterally 2. Lateral rectus muscle. Left eye can't move laterally 3. The left superior rectus muscle. The left eye can't move upward 4. Inferior oblique muscle. Left eye can't move upward and laterally. (b) Anterior view of the right eye QUESTION 13

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2. Derive the equation of motion for the system shown. The oscillation is defined by the displacement $x$ measured from the equilibrium position of the block. The pulley's moment of inertia about its pinned center is $J$. Determine the natural frequency and damping ratio of the system. Ans: $\zeta = \frac{25c}{12\sqrt{k(m + J/(9r^2))}}$

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c) A data acquisition system has the following signals at its input: 40Hz, 70Hz, 30Hz, 100Hz, and 90Hz. Design an anti-aliasing filter for the data acquisition system. [5 Marks] d) Derive the transfer function of a PI controller (Clearly showing the constants of proportionality in terms of resistances and capacitance given in figure Q7.) [7 Marks]

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