Question

The range of tides is affected by the relative positions of the sun and the moon. The highest high tides and the lowest low tides occur during the new moon and full moon. During the first and third quarters of the lunar month, the lowest high tides and highest low tides occur. Throughout the month, the tidal range gradually increases and decreases between the minimum and maximum values of the range.

7) Based on the information above, at what time would the difference between the highest y value and the lowest y value of the tide values be the greatest?

Answer 1

@Michele_Laino

Answer 2

Hi

Answer 3

hi @ganeshie8 could you help me?

Answer 4

@welshfella

Answer 5

@Michele_Laino

Answer 6

The y-values are the tides, correct? What are the x-values?

Answer 7

not sure @Aveline

Answer 8

The x-values are the phases of the moon. The tides, or y-values, are dependent on the x-values, or the phases of the moon.

Answer 9

When are the tides highest and lowest?

Answer 10

so biggest difference is when there is a new moon or full moon?

Answer 11

@Aveline

Answer 12

You are correct

Answer 13

Based on the information above, at what time would the difference between the highest y value and the lowest y value of the tide values be the lowest?

Answer 14

"During the first and third quarters of the lunar month, the lowest high tides and highest low tides occur."

Answer 15

first and third quarters of a lunar month?

Answer 16

Yup :)

Answer 17

ok i have four more questions that i have all parts figured out but 1 in each of them. could you help with them?

Answer 18

Sure

Answer 19

Sorry I have a test so I'll brb

Answer 20

give the a) period, b) amplitude, and c) difference between the highest y value and the lowest y value of each of the periodic functions given below. The periods are all either in terms of π or decimal values in these examples, but you may round to the nearest integer if you prefer.

Answer 21

@Michele_Laino

Answer 22

i just need this
The periods are all either in terms of π or decimal values in these examples, but you may round to the nearest integer if you prefer.

Answer 23

"The period is the distance required for the function to complete one full cycle"

Answer 24

for first function, we have to solve this equation, for \(T\) (\(T\) is the unknown period)
\[\cos \left( {3\left( {x + T} \right)} \right) = \cos \left( {3x} \right)\]

Answer 25

i onow but how do i put it in terms of pi

Answer 26

@Michele_Laino please come back we're not done.. :)

Answer 27

i thought the period was 2 but that isnt in terms of pi

Answer 28

You don't need to put them in terms of pi I don't think...?
"The periods are all either in terms of π or decimal values"?

Answer 29

devloping the left side, we get:
\[\cos \left( {3x} \right)\cos \left( {3T} \right) - \sin \left( {3x} \right)\sin \left( {3T} \right) = \cos \left( {3x} \right)\]

Answer 30

and the solution, is:
\[\begin{gathered}
\cos \left( {3T} \right) = 1 \hfill \\
\sin \left( {3T} \right) = 0 \hfill \\
\end{gathered} \]

Answer 31

so would 2 be right as the period for the first one?

Answer 32

solving the equation:
\[\cos \left( {3T} \right) = 1\]
we get, as the littlest solution:
\(3T=2 \pi\)
please solve for \(T\)

Answer 33

Well, the equation is cos(3x)
I would just use 2pi/b or 2pi/3 even though the graph doesn't look the same.

Answer 34

2.09439510239

Answer 35

so what would i do to put it in pi terms

Answer 36

please in terms of \(\pi\) @18jonea

Answer 37

Don't bother to simplify, just write \[\frac{ 2\pi }{ 3 }\]

Answer 38

so that would be the period for the first one?

Answer 39

if we divide both sides by \(3\), we get:
\[\frac{{3T}}{3} = \frac{{2\pi }}{3}\]
please simplify

Answer 40

Correct. Can you figure out the second one? Just put 2pi/b

Answer 41

how do you simplify 2pi/3

Answer 42

You don't. It's already in terms of pi

Answer 43

@Michele_Laino said to simplify

Answer 44

hint: