2 years ago

2. The city council is planning a long narrow park with a playground at one end and a fountain at the other.

Mathematics

1 answer:

vivado [14]2 years ago

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Answer:

Step-by-step explanation:

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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

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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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Use Pythagoras theorem
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