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jarptica [38.1K]
3 years ago
8

Pls help I will mark brainliest if it’s right

Mathematics
1 answer:
vladimir2022 [97]3 years ago
3 0

Answer:

C

Step-by-step explanation:

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\bold{Answer:\quad y=-3\cos\bigg(\dfrac{\pi}{20}x\bigg)+5}

<u>Step-by-step explanation:</u>

Use the formula y = A cos (Bx - C) + D    where

  • A = amplitude
  • Period = 2π/B
  • Phase Shift = C/B
  • D = vertical shift (aka midline)

Given: Max = 8, Min = 2, (1/2)Period = 20 → Period = 40

Amplitude (A) = (Max - Min)/2

                      = (8 - 2)/2

                      = 6/2

                      = 3

Midline (D) = (Max + Min)/2  

                  = (8 + 2)/2

                  = 10/2

                  = 5

Period = 2π/B    

→ B = 2π/Period

      = 2π/40

      = π/20

Notice that the Minimum touches the y-axis (not the Max) so there is no phase shift but there is a reflection → C-value = 0 & A-value is negative

Now, let's put it all together:

A = -3, B = π/20, C = 0, D = 5

\large\boxed{y=-3\cos\bigg(\dfrac{\pi}{20}x\bigg)+5}

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