Please help answer Noah’s incorrect claim

Mathematics

1 answer:

PolarNik [594]3 years ago

5 0

Answer:

a subset of integers

Step-by-step explanation:

You have to look at the definition of the variable and the meaning of the function value in order to determine suitable domain values.

Here, the variable is defined as a number of dimes. It must be a non-negative integer, a subset of the integers. (We cannot count fractional dimes or negative dimes.)

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Since the variable represents "a handful of dimes", there must be an upper limit on its value. We expect that it will be something less than 1000 (20 rolls of dimes), but it might be slightly more.

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3 years ago

What is partial derivative of z=(2x+3y)^10 with respect to x,y?

maw [93]

Not sure if you mean to ask for the first order partial derivatives, one wrt x and the other wrt y, or the second order partial derivative, first wrt x then wrt y. I'll assume the former.

$\dfrac\partial{\partial x}(2x+3y)^{10}=10(2x+3y)^9\times2=20(2x+3y)^9$

$\dfrac\partial{\partial y}(2x+3y)^{10}=10(2x+3y)^9\times3=30(2x+3y)^9$

Or, if you actually did want the second order derivative,

$\dfrac{\partial^2}{\partial y\partial x}(2x+3y)^{10}=\dfrac\partial{\partial y}\left[20(2x+3y)^9\right]=180(2x+3y)^8\times3=540(2x+3y)^8$

and in case you meant the other way around, no need to compute that, as $z_{xy}=z_{yx}$ by Schwarz' theorem (the partial derivatives are guaranteed to be continuous because $z$ is a polynomial).