Afarmer has 140 bushels of wheat to sell at her roadside stand. she sells an average of 16 1/5 bushels each day. represent the total change in the number of bushels he has for sale after 7 days.

Jackie purchased 3 bottles of water and 2 cups of coffee for a family for $7.35. brian bought 4 bottles of water and 1 cup of coffee for his family for $7.15. how much does each bottle of water cost? how much does each cup of coffee cost? i need this done

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

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