Question (1 point) Solve the IVP day dy + 8 +80y= 0, y(0) = 0,4'(0) = 9 dt2 dt The Laplace transform of the solutions is L{y} = 9/((s^2)+8s+80) By completing the square in the denominator we see that this is the Laplace transform of shifted by the rule (Your first answer blank for this question should be a function of t). Therefore the solution is y =

In Exercises 3-34, evaluate the given definite integrals. 3. \( \int_{0}^{3} 6 x d x \) 4. \( \int_{0}^{2} 4 x^{3} d x \) 5. \( \int_{1}^{4} x^{5 / 2} d x \) 6. \( \int_{4}^{9}\left(p^{3 / 2}-3\right) d p \) 7. \( \int_{3}^{6}\left(\frac{1}{\sqrt{x}}-7\right) d x \) 8. \( \int_{1.2}^{1.6}\left(5+\frac{6}{x^{4}}\right) d x \) 9. \( \int_{-1.6}^{0.7}(1-x)^{1 In Exercises 3-34, evaluate the given definite integrals. 3. \( \int_{0}^{3} 6 x d x \) 4. \( \int_{0}^{2} 4 x^{3} d x \) 5. \( \int_{1}^{4} x^{5 / 2} d x \) 6. \( \int_{4}^{9}\left(p^{3 / 2}-3\right) d p \) 7. \( \int_{3}^{6}\left(\frac{1}{\sqrt{x}}-7\right) d x \) 8. \( \int_{1.2}^{1.6}\left(5+\frac{6}{x^{4}}\right) d x \) 9. \( \int_{-1.6}^{0.7}(1-x)^{1 / 3} d x \) 10. \( \int_{1}^{5} \sqrt{3 v+1} d v \) 11. \( \int_{-2}^{2}(T-2)(T+2) d T \) 12. \( \int_{1}^{2}\left(3 x^{5}-2 x^{3}\right) d x \) 13. \( \int_{0.5}^{2.2}(\sqrt[3]{x}-2) d x \) 14. \( \int_{2.7}^{5.3}\left(\frac{1}{x \sqrt{x}}+4\right) d x \)

630t + 1 The sales of a math performance enhancing drug are given by S(t) = where t is in years and S(t) is in millions of dollars. What is the rate of change of sales in millions of dollars per year when t = 0? t2 + 9 S'(0) = x millions of dollars per year.

Find a vector a with representation given bythe directed line segment AB. DrawAB and the equivalent representationstarting at the origin.a) A(-2,-2), B(5,3)b) A(4,0,-2), B(4,2,1)

Sweet Catering completed the following selected transactions during May 2016: Sweet Catering completed the following selected transactions during May 2016: • May 5: Received and paid electricity bill, $120 May 9: Received cash for meals served to customers, $3,190 • May 23: Served a banquet on account, $2,540 • May 31: Accrued salary expense, $750 • May 31: Recorded prepaid insurance expired, $170 If Sweet Catering had recorded transactions using the Cash method, how much net income (loss) would they have recorded for the month of May? If there is a loss, enter it with parentheses or a negative sign. If Sweet Catering had recorded transactions using the Accrual method, how much net income (loss) would they have recorded for the month of May? If there is a loss, enter it with parentheses or a negative sign.

14.1 Match the terms in the left column with their definitions from the right column: 1. Bill of materials a. A factor that causes costs to change 2. Operations list b. A measure of the number of good units produced in a period of time c. A list of the raw materials used to create a finished product 3. Master production schedule 4. Lean manufacturing d. A document used to authorize removal of raw materials from inventory 5. Production order e. A cost accounting method that assigns costs to products based on specific processes performed 6. Materials requisition f. A cost accounting method that assigns costs to specific batches or production runs and is used when the product or service consists of uniquely identifiable items 7. Move ticket g. A cost accounting method that assigns costs to each step or work center and then calculates the average cost for all products that passed through that step or work center 8. Job-time ticket h. A document that records labor costs associated with manufacturing a product 9. Job-order costing i. A document that tracks transfer of inventory from one work center to another 10. Cost driver j. A document that authorizes manufacture of a finished good 11. Throughput k. A document that lists the steps required to manufacture a finished good 1. A document that specifies how much of a finished good is to be produced during a specific time period 12. Computer-integrated manufacturing m. A production planning technique that is an extension of the just-in-time inventory control method n. A production planning technique that is an extension of the materials requirement planning inventory control method o. A term used to refer to the use of robots and other IT techniques as part of the production process

11.60 Consider the flow of air through the piping system shown in Fig. P11.60. If the system is choked, determine the location where the Mach number is 1. Calculate the pressure ratio pb/Po, that causes choking in this system. 100 in 100 in Pв PO то 4 1.5 in diameter 1 in diameter Short nozzle 0.0030 in 1.5 in pipe 0.0035 in 1 in pipe