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3 years ago

Is this equation linear or nonlinear?y =x/2

Mathematics

1 answer:

user100 [1]3 years ago

3 0

Answer:

linear

Step-by-step explanation:

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This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the ex

olga nikolaevna [1]

$f(x_1,\ldots,x_n)=x_1+\cdots+x_n=\displaystyle\sum_{i=1}^nx_i$

${x_1}^2+\cdots+{x_n}^2=\displaystyle\sum_{i=1}^n{x_i}^2=4$

The Lagrangian is

$L(x_1,\ldots,x_n,\lambda)=\displaystyle\sum_{i=1}^nx_i+\lambda\left(\sum_{i=1}^n{x_i}^2-4\right)$

with partial derivatives (all set equal to 0)

$L_{x_i}=1+2\lambda x_i=0\implies x_i=-\dfrac1{2\lambda}$

for $1\le i\le n$ , and

$L_\lambda=\displaystyle\sum_{i=1}^n{x_i}^2-4=0$

Substituting each $x_i$ into the second sum gives

$\displaystyle\sum_{i=1}^n\left(-\frac1{2\lambda}\right)^2=4\implies\dfrac n{4\lambda^2}=4\implies\lambda=\pm\frac{\sqrt n}4$

Then we get two critical points,

$x_i=-\dfrac1{2\frac{\sqrt n}4}=-\dfrac2{\sqrt n}$

$x_i=-\dfrac1{2\left(-\frac{\sqrt n}4\right)}=\dfrac2{\sqrt n}$

At these points we get a value of $f(x_1,\cdots,x_n)=\pm2\sqrt n$ , i.e. a maximum value of $2\sqrt n$ and a minimum value of $-2\sqrt n$ .

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3 years ago

6. A cone is 10 inches tall and ha s a radius of 3 inches. What is the cone’s volume? A. 31.4 cubic inches B. 94.2 cubic inches

artcher [175]

I have no idea sorry lol

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3 years ago

What is the cube root of a27

deff fn [24]

Answer:

Your correct answer is 3

Hope this helps have an amazing day......

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What set of numbers do the following belong out of -18 and 0

ella [17]

Answer:

9 , 2 , and 6 .

Step-by-step explanation:

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3 years ago

I dont understand what to do

marta [7]

Multiply negative five over three by negative thirty three and then add thirty five which will give you the answer.

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3 years ago

Is this equation linear or nonlinear?y =x/2​

Is this equation linear or nonlinear?y =x/2