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3 years ago

Please answer correctly !!!!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!

Mathematics

2 answers:

Kisachek [45]3 years ago

8 0

Answer: 14

MNJ is angle 13 so angle 14 is the other angle that makes a straight line or 180°.

Dvinal [7]3 years ago

4 0

Answer: Angle MNO

Step-by-step explanation: Supplementary angles equal 180, or a straight line.

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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

What does the left side of the equal<br> sign simplify to?

polet [3.4K]

Answer:

Step-by-step explanation:

An expression is a mathematical statement that does not contain an equal sign. It cannot be solved for unless the value of the variable is given. An equation is a mathematical statement or sentence comprised of two equalities or expressions joined with an equal sign.

6 0

4 years ago

Read 2 more answers

Need help fast!!! 15 points!!

GrogVix [38]

C. Y = 3/10x + 1/2
....................

8 0

3 years ago

Draw the image of △ABC, under a translation by 2 units down.

balu736 [363]

Answer:

Point C would now be (6,0)

Point B would now be (0,-7)

Point A would now be (2,-6)

5 0

3 years ago

Please help with those two?

german

First question:

When you bisect an angle, you create two new equal angles, both measuring half of the original angle. So, if the original angle was 52°, the two angles will be 52/2=26 degrees each.

Note: the picture is not very clear, and I'm not sure the original angle is 52°. It it's not, just divide by 2 whatever measure the angle is.

Second question:

Focus on triangles RQP and RSP:

They are both right, because Q and S are right angles
We are given QP=SP
They share the side RP

So, they are congruent. This implies that angle SRP is 50° as well, and then

QRS = QRP+SRP = 50°+50°=100°

6 0

3 years ago