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2 years ago

Solve 4x^5-12x^4+x^3-52x^2-60x-16=0

Mathematics

1 answer:

natali 33 [55]2 years ago

3 0

Answer:

See below.

Step-by-step explanation:

4x^5 - 12x^4 + x^3 - 52x^2 - 60x - 16 = 0

The fastest way to do this is to draw a graph on paper or with software. This will give you any real solutions. For a complete solution you could then use long division and solve the quotient.

From the graph I drew there are 3 real solutions: 4 and -0.5 multiplicity 2.

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Two airplanes are flying in the air at the same height. Airplane A is flying east at 300mi/h and airplane B is flying north at 2

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Answer:

$\frac{dAB}{dt}=340 mil/h$

Step-by-step explanation:

The change of distance over time of the plain A is 300 mi/hour and 200 mi/hour for plane B. O is the point of the airport.

So, the distance from A to O AO = 90 miles and BO = 120 miles.

Now, we have a right triangle here. We can use the Pythagorean theorem, so the distance between the planes will be:

$AB^{2} =AO^{2}+BO^{2}$ (1)

$AB =\sqrt{AO^{2}+BO^{2}}=$

$AB =\sqrt{90^{2}+120^{2}}=150 miles$

If we take the derivative of the equation (1) we could find the change of the distance between planes.

$2AB\frac{dAB}{dt}=2AO\frac{dAO}{dt}+2BO\frac{dBO}{dt}$

$2*150\frac{dAB}{dt}=2*90*300+2*120*200=102000 mil/h$

$\frac{dAB}{dt}=\frac{102000}{150*2}$

Finally,

$\frac{dAB}{dt}=340 mil/h$

I hope it helps you!

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