3 years ago

Z2+4z-165=(z-11)(z+-15)

Mathematics

1 answer:

Contact [7]3 years ago

8 0

Answer: look at the picture

Step-by-step explanation: Hope this help :D

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3 years ago

Suppose a tub has the shape of an elliptical paraboloid given by z = ax2+by2 (where a, b are some positive constants). If a marb

Umnica [9.8K]

Answer:

It would roll in this direction.

$\nu = (-a/\sqrt{a^2+b^2},-b/\sqrt{a^2+b^2})$

Step-by-step explanation:

It would roll to the direction of maximum decrease, which is the -1 times the direction of maximum increase, which is given by the gradient of the function.

Since

$z = ax^2 + by^2$

For this case, the gradient of your function would be

$\nabla z = (2ax , 2by)$

And -1 times the gradient of your function would be

$-\nabla z = (-2ax , -2by)\\$

Then, at

$(1,1,a+b),\\x = 1 \\y = 1$

So it would go towards

$v = (-2a,-2b)$

The magnitud of that vector is

$|v| = 2\sqrt{a^2+b^2}$

and to conclude it would roll in this direction.

$\nu = (-a/\sqrt{a^2+b^2},-b/\sqrt{a^2+b^2})$

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3 years ago