In 1696, the first calculus textbook was published by the Marquis de l'Hôpital. The following problem is a simplified version of a problem from this text.
In Figure 2 below, we have two ropes attached to a ceiling, 3m apart. A pulley is attached to the rope on
the left, which has a length of Im. The other rope has length 5m, and it passes through the pulley and has a
weight attached to the end of it. When the weight is released, the ropes and pulley rearrange themselves so
that the diptance from the weight to the ceiling is maximized. As a simplifying assumption in this problem,
you may assume that the radius of the pulley is small enough to be negligiblo.
(a) Create an equation which gives the distance from the weight to the ceiling as a function of 0, the angle
that the Im rope makes with the ceiling.
(6) Use this to determine the value of O for which this distance is maximized.
(e) Determine the horizontal position that the weight will assume once the ropes and pulleys have adjusted
themselves to an equilibrium state.
3 meters
1 meter
Weight

Calculate the monthly payment for a $2,500 loan at 9% annual interest for two years. use the formula, m = pm(1 + m)^na/(1 + m)^na - 1 as needed. a. $85.15 b. $105.40 c. $114.21 d. $125.72 calculate the total payback for a $2,500 loan at 9% annual interest for two years. use the formula, m = pm(1 + m)^na/(1 + m)^na - 1 as needed. a. $1,021.80 b. $1,370.52 c. $2,043.60 d. $2,741.04 alice wants to use the stack method to pay down her debts listed in the table below. if she applies an extra $150 a month to her debts, what will be the second debt she targets to pay off and what will be the monthly amount she applies to it? debts interest rate minimum monthly payment debt 1 5.5% $75 debt 2 2.75% $250 debt 3 13.25% $150 a. debt 1, $225 b. debt 1, $375 c. debt 3, $300 d. debt 3, $400 at greenbrier bank, checking account customers earn 0.8% interest a month on their account balances, pay a $0.10 service fee per check, and pay a monthly $2.00 financial charge. calculate the income earned on the checking account for a customer who writes 21 checks and maintains a minimum balance of $1,210. a. $4.27 b. $5.58 c. $6.42 d. $7.35 which statement most accurately compares debit and credit cards? a. both cards deduct from funds currently in a checking account. b. both cards use funds temporarily loaned from a financial institution. c. both cards are processed by the same card system services. d. both carry the risk of overdraft.

He that is measured at 220° is a reflex angle. the opposite angle is obtuse. find the measure of obtuse .

Which graph represents the parent function of y=(x+2)(x-2)