What’s 20.72 + 2.027

I don't know what this is. please, help me.

nikitadnepr [17]

The answer is a) 12m^3 + 10n^2

7 0

3 years ago

6.<br> A. y=-13x1<br> or B. y = 1-3xl

IrinaVladis [17]

Answer: B

Step-by-step explanation

6 0

3 years ago

guse lagrange multipliers to find the maximum or minimum values of the function subject to the given constraint. (if an answer d

Novosadov [1.4K]

Therefore the maximum value of function f(x,y,z)= $x^{2} y^{2} z^{2}$ =1/27

And the minimum value is 0

<h3>What is function?</h3>

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable) (the dependent variable) (the dependent variable). Mathematics uses functions frequently, and functions are essential for specifying physical relationships in the sciences.

Here,

The function is given as:

f(x,y,z)= $x^{2} y^{2} z^{2}$

$x^{2} +y^{2}+ z^{2}$ =1

=> $x^{2} +y^{2}+ z^{2}$ -1=0

Using Lagrange multiplies, we have:

L(x,y,z,λ)=f(x,y,z) +λ(0)

Substitute f(x,y,z)= $x^{2} y^{2} z^{2}$ and $x^{2} +y^{2}+ z^{2}$ -1=0

Differentiate

L(x)= $2xy^{2} z^{2}$ +2λx

L(y)= $2yx^{2} z^{2}$ +2λy

L(z)= $2zx^{2} y^{2}$ +2λz

L(λ)= $x^{2} +y^{2}+ z^{2}$ -1

Equating to 0

$2xy^{2} z^{2}$ +2λx =0

$2yx^{2} z^{2}$ +2λy = 0

$2zx^{2} y^{2}$ +2λz = 0

$x^{2} +y^{2}+ z^{2}$ -1 = 0

Factorize the above expressions

$2xy^{2} z^{2}$ +2λx =0

2x( $y^{2} z^{2}$ +λ)=0

2x=0 and ( $y^{2} z^{2}$ +λ)=0

x=0 and $y^{2} z^{2}$ = -λ

$2yx^{2} z^{2}$ +2λy = 0

2y( $x^{2} z^{2}$ +λ)=0

2y=0 and ( $x^{2} z^{2}$ +λ)=0

y=0 and $x^{2} z^{2}$ = -λ

$2zx^{2} y^{2}$ +2λz = 0

2z( $y^{2} x^{2}$ +λ)=0

2z=0 and ( $x^{2} y^{2}$ +λ)=0

z=0 and $x^{2} y^{2}$ = -λ

So we have ,

x=0 and $y^{2} z^{2}$ = -λ

y=0 and $x^{2} z^{2}$ = -λ

z=0 and $x^{2} y^{2}$ = -λ

The above expression becomes

x=y=z=0

This means that,

$x^{2} +y^{2}+ z^{2}$ =1

$x^{2} +x^{2}+ x^{2} =1 \\3x^{2 } =1$

x= ±1/ $\sqrt{3}$

So,

y= ±1/ $\sqrt{3}$

z= ±1/ $\sqrt{3}$

The critic points are

x=y=z=±1/ $\sqrt{3}$

x=y=z=0

Therefore the maximum value of function f(x,y,z)= $x^{2} y^{2} z^{2}$ =1/27

And the minimum value is 0

To know more about function , visit

brainly.com/question/12426369

#SPJ4

3 0

1 year ago

Solve. 4x−y−2z=−8 −2x+4z=−4 x+2y=6 Enter your answer, in the form (x,y,z), in the boxes in simplest terms. x= y= z=

ladessa [460]

Answer:

(-2, 4, -2)

x=-2, y=4, z=-2.

Step-by-step explanation:

So we have the three equations:

$4x-y-2z=-8\\-2x+4z=-4\\x+2y=6$

And we want to find the value of each variable.

To solve this system, first look at it and consider what you should try to do.

So we can see that the second and third equations both have an x.

Therefore, we can isolate the variables for the second and third equation and then substitute them into the first equation to make the first equation all xs.

Therefore, let's first isolate the variable in the second and third equation.

Second Equation:

$-2x+4z=-4$

First, divide everything by -2 to simplify things:

$x-2z=2$

Subtract x from both sides. The xs on the left cancel:

$(x-2z)-x=2-x\\-2z=2-x$

Now, divide everything by -2 to isolate the z:

$z=-\frac{2-x}{2}$

So we've isolated the z variable. Now, do the same to the y variable in the third equation:

$x+2y=6$

Subtract x from both sides:

$2y=6-x$

Divide both sides by 2:

$y=\frac{6-x}{2}$

Now that we've isolated the y and z variables, plug them back into the first equation. Therefore:

$4x-y-2z=-8\\4x-(\frac{6-x}{2})-2(-\frac{2-x}{2})=-8$

Distribute the third term. The -2s cancel out:

$4x-(\frac{6-x}{2})+(2-x)=-8$

Since there is still a fraction, multiply everything by 2 to remove it:

$2(4x-(\frac{6-x}{2})+(2-x))=2(-8)$

Distribute:

$8x-(6-x)+2(2-x)=-16\\8x-6+x+4-2x=-16$

Combine like terms:

$8x+x-2x-6+4=-16\\7x-2=-16$

Add 2 to both sides:

$7x=-14$

Divide both sides by 7:

$(7x)/7=(-14)/7\\x=-2$

Therefore, x is -2.

Now, plug this back into the second and third simplified equations to get the other values.

Second equation:

$z=-\frac{2-x}{2}\\ z=-\frac{2-(-2)}{2}\\z=-\frac{4}{2}\\z=-2$

Third equation:

$y=\frac{6-x}{2}\\y=\frac{6-(-2)}{2}\\y=\frac{8}{2}\\y=4$

Therefore, the solution is (-2, 4, -2)

3 0

3 years ago

Read 2 more answers

Sara plotted the locations of the trees in a park on a coordinate grid. She plotted an oak tree which was in the middle of the p

padilas [110]

Answer: $10.2\ yards$

Step-by-step explanation:

<h3> "Sara plotted the locations of the trees in a park on a coordinate grid. She plotted an oak tree, which was in the middle of the park, at the origin. She plotted a maple tree, which was 10 yards away from the oak tree, at the point (10,0) . Then she plotted a pine tree at the point (-2.4, 5) and an apple tree at the point (7.8, 5) What is the distance, in yards, between the pine tree and the apple tree in the</h3><h3>park?"</h3>

For this exercise you need to use the following formula, which can be used for calculate the distance between two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

In this case, you need to find distance, in yards, between the pine tree and the apple tree in the park.

You know that pine tree is located at the point (-2.4, 5) and the apple tree is located at the point (7.8, 5).

So, you can say that:

$x_2=-2.4\\x_1=7.8\\\\y_2=5\\y_1=5$

Knowing these values, you can substitute them into the formula and then evaluate, in order to find the distance, in yards, between the pine tree and the apple tree in the park.

This is:

$d=\sqrt{(-2.4-7.8)^2+(5-5)^2}=10.2\ yards$

8 0

3 years ago