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3 years ago

HELPPPP!!!

Mathematics

1 answer:

Anuta_ua [19.1K]3 years ago

3 0

Answer:

A = √29

Step-by-step explanation:

The short of it is that ...

A² = 2² + 5² = 29

A = √29

_____

<u>Amplitude</u>

If you expand the second form using the sum-of-angles formula, you get ...

Asin(ωt +φ) = Asin(ωt)cos(φ) +Acos(ωt)sin(φ)

Comparing this to the first form, you find ...

c₂ = 2 = Acos(φ)

c₁ = 5 = Asin(φ)

The Pythagorean identity can be invoked to simplify the sum of squares:

(Asin(φ))² + (Acos(φ))² = A²(sin(φ)² +cos(φ)²) = A²·1 = A²

In terms of c₁ and c₂, this is ...

(c₁)² +(c₂)² = A²

A = √((c₁)² +(c₂)²) . . . . . . . formula for amplitude

_____

<u>Phase Shift</u>

We know that tan(φ) = sin(φ)/cos(φ) = (Asin(φ))/(Acos(φ)) = 5/2, so ...

φ = arctan(c₁/c₂) . . . . . . . formula for phase shift*

φ = arctan(5/2) ≈ 1.19029 radians

___

* remember that c₁ is the coefficient of the cosine term, and c₂ is the coefficient of the sine term.

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Which line(s) intersect the parabola y = x^2 − 3x + 4 at two points? Select all that apply. A. y = –3x + 2 B. y = –3x + 3 C. y =

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Step-by-step explanation:

Equating the line A and the parabola, we get

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Equating the line B and the parabola, we get

-3x + 3 = x² - 3x + 4

0 = x² - 3x + 4 + 3x - 3

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which has no real solutions. Then, the line B and the parabola don't intersect each other.

Equating the line C and the parabola, we get

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0 = x² - 3x + 4 + 3x - 5

0 = x² - 1

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