Question   \[ \text { LET } f(x)=\ln (3 x+5) \] SHOW BY MATHEMATICAL \[ \begin{array}{l} \text { INDUCTION MATIEMATH THT } \\ \text { THE } n^{\text {th }} \text { DERIVATIVE } \\ \text { OF } f \text { IS GIVEN BY } \\ f^{(n)}(x)=\frac{(-1)^{n+1} 3^{n}(n+1) !}{(3 x+5)^{n}} \end{array} \] For all INTEGERS \( h \geqslant 1 \)

15-16 Set up iterated integrals for both orders of integration. Then evaluate the double integral using the easier order and explain why it's easier.> $\iint_{D} y d A, \quad D$ is bounded by $y=x-2, x=y^{2}$

A 2-wire d.c. distributor is 250 m long. It is to be loaded as shown in Fig 13.10 at 50 m intervals. If the maximum voltage drop is not to exceed 10V and the resistivity of core material is 0-7 x 2-54 2 cm, [1-602 cm'] determine the maximum cross-sectional area of each conductor. Supply End 120 A 90 A 60 A 50 A 80 A

A 115kv 3-phase transposed transmission line is composed of 2-ACSR 336, 400 сmil, 30/7 Oriole conductors per phase with horizontal configuration. Dx2 =7ft, Dz3 = 7ft, D:3 = 14ft. The line spacing is measured from the center of the bundled conductors. The distance between the conductors of the bundle is 6 inches. The conductors have a diameter of 0.741 inch and a GMR of 0.02255ft. Find the capacitance per phase for 20km of line in microfarad.

Chapter 13, Section 13.6, Question 081 Given that the directional derivative of f (x, y, z) at the point (5, -7,7) in the direction of a = 3i – 2j - 6k is -10 and that || Vf (5, -7,7)|| = 10, find Vf (5, -7,7). Vf (5, -7, 7) = ( ? Edit ? Edit )i+( ? Edit)j +( ? Edit k.

Taylor’s is a popular restaurant that offers customers a large dining room and comfortable bar area. Taylor Henry, the owner and manager of the restaurant, has seen the number of patrons increase steadily over the last two years and is considering whether and when she will have to expand its available capacity. The restaurant occupies a large home, and all the space in the building is now used for dining, the bar, and kitchen, but space is available on the property to expand the restaurant. The restaurant is open from 6 p.m. to 10 p.m. each night (except Monday) and, on average, has 24 customers enter the bar and 50 enter the dining room during each of those hours. Taylor has noticed the trends over the last 2 years and expects that within about 4 years, the number of bar customers will increase by 50% and the dining customers will increase by 20%. Taylor is worried that the restaurant will be not be able to handle the increase and has asked you to study its capacity. In your study, you consider four areas of capacity: the parking lot (which has 80 spaces), the bar (54 seats), the dining room (100 seats), and the kitchen. The kitchen is well-staffed and can prepare any meal on the menu in an average of 12 minutes per meal. The kitchen, when fully staffed, is able to have up to 20 meals in preparation at a time, or 100 meals per hour (60 min/12 min × 20 meals). To assess the capacity of the restaurant, you obtain the additional information: Diners typically come to the restaurant by car, with an average of 3 persons per car, while bar patrons arrive with an average of 1.5 persons per car. Diners, on average, occupy a table for an hour, while bar customers usually stay for an average of 2 hours. Due to fire regulations, all bar customers must be seated. The bar customer typically orders one drink per hour at an average of $7 per drink; the dining room customer orders a meal with an average price of $22; the restaurant’s cost per drink is $1, and the direct costs for meal preparation are $5. Required: a. Given the current number of customers per hour, what is the amount of excess capacity in the bar, dining room, parking lot, and kitchen? b. Calculate the expected total throughput margin for the restaurant per day, and month (assuming a 26-day month). a. Given the expected increase in the number of customers, determine if there is a constraint for any of the four areas of capacity. What is the amount of needed capacity for each constraint? b. If there is a constraint, reduce the demand on the constraint so that the restaurant is at full capacity (assume some customers would have to be turned away). Calculate the expected total throughput margin for the restaurant per day, and month (assuming a 26-day month). Taylor has obtained construction estimates. To increase the capacity of the bar to 80 seats, the dining room to 120 seats, and the kitchen to 25 meals at the same time would cost $250,000, which Taylor could finance for $5,000 per month for the next 4 years. There would be no change to the parking lot. Given your analysis above, prepare a brief recommendation to Taylor regarding expanding the restaurant.

lodine-131 is used to treat Graves disease, a disease of the thyroid gland. The amount of 131 used depends on the size of the gland. If the dose is 86 microcuries per gram of thyroid gland, how many grams of 131 should be administered to a patient with a thyroid gland weighing 19 g? Assume all the iodine administered accumulates in the thyroid gland. . X 1 g 1311