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3 years ago

12

What is the slope, m, and y-intercept for the line that is plotted on the grid below? On a coordinate plane, a line goes through

points (0, 4) and (negative 2, 0). m = One-half, (0, –2) m = One-half, (0, 4) m = 2, (0, –2) m = 2, (0, 4)

2 answers:

Snowcat [4.5K]3 years ago

9 0

Answer:

m = 2, (0, –2) Im 90% sure

Step-by-step explanation:

I just took the test :)

cricket20 [7]3 years ago

6 0

Answer:

m = 2, (0, –2) Im 90% sure

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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

denis23 [38]

Hello!

<u><em>Answer: </em></u>

<u><em>1. =-6</em></u>

<u><em>2. =39</em></u>

<u><em>3. =-603</em></u>

_________________________________________________

Explanation: This question's it's about the order of operations. It stands for p-parenthesis, e-exponents, m-multiply, d-divide, a-add, and s-subtract. It can also go left to right. (PEMDAS)

1. -4(3-1)+2

Do parenthesis first.

$(3-1)=2$

$-4*2+2$

Then do multiply left to right.

$-4*2=-8$

Add left to right.

$-8+2$

$8-2=6$

*Answer should be have negative sign.*

Answer: → $\boxed{=-6}$

______________________________________________________

2. 3⋅[(30−8)÷2+2]

Do parenthesis first.

$(30-8)=22$

$22/2+2$

Then divide left to right.

$22/2=11$

Add left to right.

$11+2=13$

Multiply left to right.

$3*13=39$

*Answer should be have positive sign.*

Answer: → $\boxed{=39}$

_____________________________________________________

3. 14(1-23)2+13

Do parenthesis first.

$(1-23)=-22$

$14(-22)*2+13$

Then, you multiply left to right.

$14(-22)=-308$

$-308*2=-616$

Add/subtract left to right.

$-616+13$

$616-13=603$

*The answer must be have a negative sign*

Answer: → $\boxed{=-603}$

____________________________________________________________

Hope this helps!

Thank you!

Have a great day!

-Charlie

7 0

3 years ago