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Dvinal [7]
2 years ago
5

Which of the following is a polynomial with roots 4, 2i, and −2i?

Mathematics
2 answers:
ivolga24 [154]2 years ago
3 0
Hello,

(x+2i)(x-2i)(x-4)=(x²+4)(x-4)=x^3-4x²+4x-16

Answer C
maks197457 [2]2 years ago
3 0
X = 4; x = 2i; x = -2i

f(x) = (x - 4)(x - 2i)[x - (-2i)] = (x - 4)\underbrace{(x-2i)(x+2i)}_{a^2-b^2=(a-b)(a+b)}\\\\=(x-4)[x^2-(2i)^2]=(x-4)(x^2-2^2i^2)=(x-4)[x^2-4(-1)]\\\\=(x-4)(x^2+4)=(x)(x^2)+(x)(4)-(4)(x^2)-(4)(4)\\\\=x^3+4x-4x^2-16=\boxed{x^3-4x^2+4x-16}


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A guitar string is plucked at a distance of 0.6 centimeters above its resting position and then released, causing vibration. The
liubo4ka [24]

Answer:

The equation that represents the motion of the string is given by:

y =Ae^{-kt}\cos(2\pi ft)     .....[1] where t represents the time in second.

Given that: A = 0.6 cm (distance above its resting position) , k = 1.8(damping constant) and frequency(f) = 105 cycles per second.

Substitute the given values in [1] we get;

y =0.6e^{-1.8t}\cos(2\pi 105t)  

or

y =0.6e^{-1.8t}\cos(210\pi t)  

(a)

The trigonometric function that models the motion of the string is given by:

y =0.6e^{-1.8t}\cos(210\pi t)

(b)

Determine the amount of time t that it takes the string to be damped so that -0.24\leq y \leq0.24

Using graphing calculator for the equation

y =0.6e^{-1.8x}\cos(210\pi x)

let x = t (time in sec)  

Graph as shown below in the attachment:

we get:

the amount of time t that it takes the string to be damped so that -0.24\leq y \leq0.24 is, 0.5 sec


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If arc AD = 62° and arc BC = 28°, then what is the measure of angle AED?
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