Ocean tides are an example of periodic behavior. at a particular harbor, data was collected over the course of
24 hours to create the following model: y = 1.236 sin / 3x) + 1.798, which gives the water level, y, in feet above
the mllw (mean lower low water) as a function of the time, x, in hours.
a. how many periods are there each day?
b. write a function that gives the time in hours as a function of the water level. how many other times per day
will have the same water levels as those given by the function?

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

i would love   to but there is no graph shown

step-by-step explanation:

i am so sorry

x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81

yes, i think so although i am not sure. this is a very strange question.