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3 years ago

Pls help solve a and b

Mathematics

1 answer:

Varvara68 [4.7K]3 years ago

6 0

A is 9 for the proportion part but I can’t see the rest of b so I can’t answer that for you

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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

1. Chapter ma2pe08r, Section .72, Problem 012 (ID: 012.07.2 - MC - MANK08) David tunes pianos in his spare time for extra income

nydimaria [60]

Answer:

Option C. $30

Step-by-step explanation:

As per question buyers are willing to pay $135 per tuning. If David demands more than this amount producer will not choose David to tune.

As we can see on first week David is willing to tune the first piano for $115,

So surplus for producer will be

135 - 115 = $20

Surplus for second week for producer will be

135 - 125 = $10

Since David is willing to tune the third and fourth piano for $140 and $175 then the producer will not choose David for tuning.

Therefore, total surplus for the producer will be $20 + $10 = $30

Option C. $30 is the correct option.

3 0

3 years ago

The base of the triangle is 4 times the height . If the area is 338 square feet, then what is the height of the triangle in feet

Inessa05 [86]

Answer:

Step-by-step explanation:

7 0

3 years ago

What is the value of h(−2) when h(x)=3x+1 ?<br><br> Enter your answer in the box.

Vikentia [17]

Sub -2 for x
h(-2)=3(-2)+1
h(-2)=-6+1
h(-2)=-5

3 0

3 years ago

Read 2 more answers

2 5/7 as a decimal. How do you figure out?

weqwewe [10]

2 5/7 as a decimal is approximately 2.70

We know that the ones place will be a two. That doesn’t change when you convert. Next you need to divide 100 by 7, which equals 14. Then you need to do 14 times 5, which equals 70. So, now you know the values after the decimal point (.70). Combine that with the whole number 2 to get 2.70.

8 0

3 years ago