A120-ton tugboat is moving at 6 ft/s with a slack towing cable attached to a 100-ton barge which is at rest. the cable is being unwound from a drum on the tugboat at a constant rate of 5.4 ft/s and that rate is maintained after the cable becomes taut. neglecting the resistance of the water, determine (a) the velocity of the tugboat after the cable becomes taut, (b) the impulse exerted on the barge as the cable becomes taut.

Annuity payments are assumed to come at the end of each payment period (termed an ordinary annuity). however, an exception occurs when the annuity payments come at the beginning of each period (termed an annuity due). what is the future value of a 13-year annuity of $2,800 per period where payments come at the beginning of each period? the interest rate is 9 percent. use appendix c for an approximate answer, but calculate your final answer using the formula and financial calculator methods. to find the future value of an annuity due when using the appendix tables, add 1 to n and subtract 1 from the tabular value. for example, to find the future value of a $100 payment at the beginning of each period for five periods at 10 percent, go to appendix c for n = 6 and i = 10 percent. look up the value of 7.716 and subtract 1 from it for an answer of 6.716 or $671.60 ($100 × 6.716)

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Camilo is a self-employed roofer. he reported a profit of $30,000 on his schedule c. he had other taxable income of $5,000. he paid $3,000 for hospitalization insurance. his self-employment tax was $4,656. he paid his former wife $4,000 in court-ordered alimony and $4,000 in child support. what is the amount camilo can deduct in arriving at adjusted gross income (agi)?