Valeria is playing with her accordion. the length of the accordion a ( t ) a(t) (in cm cm) after she starts playing as a function of time t t (in seconds) can be modeled by a sinusoidal expression of the form a ⋅ cos ⁡ ( b ⋅ t ) + d a⋅cos(b⋅t)+d. at t = 0 t=0, when she starts playing, the accordion is 1 5 cm 15 cm long, which is the shortest it gets. 1 . 5 1.5 seconds later the accordion is at its average length of 2 1 cm 21 cm. find a ( t ) a(t).

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step-by-step explanation:

1. a^4+8a^3+24a^2+32a+16

2.y^8+8y^7+28y^6+56y^5+70y^4+56y^3+28y^2+8y+1

3.x^6-3x^4y^2+3x^2y^4-y^6

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