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Naya [18.7K]
1 year ago
15

What is the midline equation of y = -4sin (2x - 7) + 3?

Mathematics
2 answers:
Georgia [21]1 year ago
4 0

Answer:

y = 3.

Step-by-step explanation:

The minimum and maximum value of \sin(2\, x - 7) over all real x are (-1) and 1, respectively. Hence, the maximum and minimum value of y = -4\, \sin(2\, x - 7) + 3 would be:

  • Maximum: y = (-4)\, (-1) + 3 = 7.
  • Minimum: y = (-4)\, (1)\ + 3 = (-1).

The midline equation of a sine wave is a horizontal line that is right in the middle of maximum and minimum y-values of that sine wave. In the sine wave in this question, the average of the maximum and minimum y\!-values is (1/2) \, (7 + (-1)) = 3. Hence, the midline equation of this sine wave would be y = 3.

AVprozaik [17]1 year ago
4 0

\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}

<h3>Given:</h3>

▪ \longrightarrow \sf{y = -4 \sin (2x - 7) + 3}

This is the equation of the horizontal line equal to the average value of <em>y</em> for the function given.

\leadsto This will correspond to the value where the sine function has a value of 0, which is the average value of the function:

\longrightarrow \sf{Y_{avg } = −4(0) + 3 = 0 + 3 = 3}

\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}

\small\bm{The \: equation\: of \: the \: midline \: is \: \:  y=3.}

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