Form a polynomial using numbers -4,4,2 with a degree of 3

Mathematics

1 answer:

shtirl [24]3 years ago

3 0

These three roots are sufficient to enable us to form a 3rd degree polynomial:

f(x) = (x+4)(x-4)(x-2) = (x^2 - 16)(x-2) = x^3 - 2x^2 - 16x + 32 (answer)

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A gold mine has two elevators, one for equipment and another for the miners. The equipment elevator descends 4 feet per second.

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Let $d_m,\ d_e$ represent the depth of the miner and equipments elevator, respectively. We know that equipment elevator descends with a velocity of $v_e = 4$ feet per second, and the miners one descends with a velocity of $v_m = 15$ feet per second.

If we start counting time ( $t=0$ ) when the equipment elevator begins to descend, after $t$ seconds its depth will be

$d_e(t) = v_et = 4t$

On the other hand, the miner elevator follows the same rule, but we have to use its velocity, and remember that it starts with a delay of thirty seconds:

$d_m(t) = v_m(t-30) = 15(t - 30)$

Now, we have to wait the 30 seconds of delay, and then another 14 seconds. This means that we want to know the positions of both elevators when $t = 44$ . Let's plug this value into the two equations: