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Annette [7]
2 years ago
5

How does g(t)=20.9t change over the interval from t=2 to t=3?

Mathematics
1 answer:
Marrrta [24]2 years ago
5 0

slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ g(t)= 20.9t\qquad \begin{cases} t_1=2\\ t_2=3 \end{cases}\implies \cfrac{g(3)-g(2)}{3-2}\implies \cfrac{20.9(3)~~ - ~~20.9(2)}{1} \\\\\\ 62.7~~ - ~~41.8\implies 20.9

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Simplest polynomial function is x^4-x^3-11x^2+9x+18.

Solution:

Given data:

Zeroes are 3i, –1, 2.

3i is a complex root of the function.

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Therefore zeroes are 3i, –3i –1, 2.

By factor theorem,

If a is zero of the function, then (x – a) is a factor of the polynomial.

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On multiplying the factors, we get the polynomial.

(x - 3i) (x + 3i) (x + 1) (x -2)

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Since the value of i^2=-1

            =x^2(x^2-x-2)-9(x^2-x-2)

            =x^4-x^3-2x^2-9x^2+9x+18

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