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Deirdre is buying plastic mugs to send to her cousin. She made a table of the various heights of stacks of different numbers of mugs.

Which equation represents the height, h, of a stack of mugs in terms of the number of mugs, t, in the stack?

A
h = 6 + 0.75(t – 1)
B
h = 6 + 0.75t
C
h = 0.75 + t(t – 1)
D
h = 0.75t – 6

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) = .

Have you ever been in the middle of telling a story and had to use hand gestures or even a drawing to make your point? in algebra, if we want to illustrate or visualize a key feature of a function, sometimes we have to write the function in a different form—such as a table, graph, or equation—to determine the specific key feature we’re looking for. think about interactions with others and situations you’ve come across in your own life. how have you had to adjust or change the way you represented something based on either the concept you were trying to describe or the person you were interacting with? explain how the complexity or layout of the concept required you to change your style or presentation, or how the person’s unique learning style affected the way you presented the information.

Maryann’s friends loved her bulletin board, and 4 of them asked her to make one for their homes. she offered to make each of her friends a replica of her bulletin board that measures 2 meters by 3 meters. how many kilograms of burlap should maryann collect to complete the bulletin boards for her friends? maryann should collect kg of burlap.