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3 years ago

9/10 + 9/10 + 9/10HELP NEEDED ASAP PLSSSSSSSSS PLSSS ILL GIVE U MAX POINTS IF U HELP PLSSSSS

Mathematics

2 answers:

Katen [24]3 years ago

8 0

Answer:

27/10

Step-by-step explanation:

n200080 [17]3 years ago

7 0

27/10 or 2 7/10 here hope this helped

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Use lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. f(x,y = xyz; x^

Snezhnost [94]

I'm assuming the constraint involves some plus signs that aren't appearing for some reason, so that you're finding the extrema subject to $x^2+2y^2+3z^2=96$ .

Set $f(x,y,z)=xyz$ and $g(x,y,z)=x^2+2y^2+3z^2-96$ , so that the Lagrangian is

$L(x,y,z,\lambda)=xyz+\lambda(x^2+2y^2+3z^2-96)$

Take the partial derivatives and set them equal to zero.

$\begin{cases}L_x=yz+2\lambda x=0\\L_y=xz+4\lambda y=0\\L_z=xy+6\lambda z=0\\L_\lambda=x^2+2y^2+3z^2-96=0\end{cases}$

One way to find the possible critical points is to multiply the first three equations by the variable that is missing in the first term and dividing by 2. This gives

$\begin{cases}\dfrac{xyz}2+\lambda x^2=0\\\\\dfrac{xyz}2+2\lambda y^2=0\\\\\dfrac{xyz}2+3\lambda z^2=0\\\\x^2+2y^2+3y^2=96\end{cases}$

So by adding the first three equations together, you end up with

$\dfrac32xyz+\lambda(x^2+2y^2+3z^2)=0$

and the fourth equation allows you to write

$\dfrac32xyz+96\lambda=0\implies \dfrac{xyz}2=-32\lambda$

Now, substituting this into the first three equations in the most recent system yields

$\begin{cases}-32\lambda+\lambda x^2=0\\-32\lambda+2\lambda y^2=0\\-32\lambda+3\lambda z^2=0\end{cases}\implies\begin{cases}x=\pm4\sqrt2\\y=\pm4\\z=\pm4\sqrt{\dfrac23}\end{cases}$

So we found a grand total of 8 possible critical points. Evaluating $f(x,y,z)=xyz$ at each of these points, you find that $f(x,y,z)$ attains a maximum value of $\dfrac{128}{\sqrt3}$ whenever exactly none or two of the critical points' coordinates are negative (four cases of this), and a minimum value of $-\dfrac{128}{\sqrt3}$ whenever exactly one or all of the critical points' coordinates are negative.

6 0

3 years ago

Which of the following best represents the average rate at which infants grow in height during the first four years after birth?

frozen [14]

Which of the following best represents the average rate at which infants grow in height during the first four years after birth? B: 3inches per year

7 0

3 years ago

Both expressions -3- (-7) and -7- (-3) involve the

Gelneren [198K]

Answer:

-3-(-7)=4 ,-7-(-3)=-4

Step-by-step explanation:

+ × += +

- × - = +

4 0

3 years ago

A robot has a straight arm 20 inches long that can rotate about the origin of a coordinate system. If the robot’s hand is locate

scoundrel [369]

Answer:

The location of the robots hand after rotating 45° counterclockwise from (-20, 0) in inches is (-14.14, 14.14)

The location of the robots hand after rotating 45° clockwise from (-20, 0)) in inches is (-14.14, -14.14)

Step-by-step explanation:

The initial location of the robots hand = (-20, 0)

The angle through which the robot rotates his hand = 45°

∴ We have the length of the robots hand = 20 inches

We note that (-20, 0) is in the 2nd Quadrant

The location of the robots hand after rotating 45° counterclockwise = 135°

Therefore, the location of the robots hand after the rotation = (20×cos(135°), 20×sin(135°)) = (-10·√2, 10·√2) = (-14.14, 14.14)

The location of the robots hand after rotating 45° clockwise from (-20, 0) = 225°

Therefore, the location of the robots hand after the rotation = (20×cos(225°), 20×sin(225°)) = (-10·√2, -10·√2) = (-14.14, -14.14)

8 0

3 years ago

What is 36 more than 40

BlackZzzverrR [31]

Answer:

Step-by-step explanation:

3 0

2 years ago

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9/10 + 9/10 + 9/10HELP NEEDED ASAP PLSSSSSSSSS PLSSS ILL GIVE U MAX POINTS IF U HELP PLSSSSS​

9/10 + 9/10 + 9/10HELP NEEDED ASAP PLSSSSSSSSS PLSSS ILL GIVE U MAX POINTS IF U HELP PLSSSSS