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3 years ago

Plz, help this do at 9:00

Mathematics

1 answer:

antoniya [11.8K]3 years ago

7 0

Answer:

Step-by-step explanation:

The answer is B no questions GO GO GO SUBTRACTION SIGN MEANS THEY OWE MONEY

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Find the minimum and maximum of f(x,y,z)=x^2+y^2+z^2 subject to two constraints, x+2y+z=4 and x-y=8.

Alika [10]

The Lagrangian for this function and the given constraints is

$L(x,y,z,\lambda_1,\lambda_2)=x^2+y^2+z^2+\lambda_1(x+2y+z-4)+\lambda_2(x-y-8)$

which has partial derivatives (set equal to 0) satisfying

$\begin{cases}L_x=2x+\lambda_1+\lambda_2=0\\L_y=2y+2\lambda_1-\lambda_2=0\\L_z=2z+\lambda_1=0\\L_{\lambda_1}=x+2y+z-4=0\\L_{\lambda_2}=x-y-8=0\end{cases}$

This is a fairly standard linear system. Solving yields Lagrange multipliers of $\lambda_1=-\dfrac{32}{11}$ and $\lambda_2=-\dfrac{104}{11}$ , and at the same time we find only one critical point at $(x,y,z)=\left(\dfrac{68}{11},-\dfrac{20}{11},\dfrac{16}{11}\right)$ .

Check the Hessian for $f(x,y,z)$ , given by

$\mathbf H(x,y,z)=\begin{bmatrix}f_{xx}&f_{xy}&f_{xz}\\f_{yx}&f_{yy}&f_{yz}\\f_{zx}&f_{zy}&f_{zz}\end{bmatrix}=\begin{bmatrix}=\begin{bmatrix}2&0&0\\0&2&0\\0&0&2\end{bmatrix}$

$\mathbf H$ is positive definite, since $\mathbf v^\top\mathbf{Hv}>0$ for any vector $\mathbf v=\begin{bmatrix}x&y&z\end{bmatrix}^\top$ , which means $f(x,y,z)=x^2+y^2+z^2$ attains a minimum value of $\dfrac{480}{11}$ at $\left(\dfrac{68}{11},-\dfrac{20}{11},\dfrac{16}{11}\right)$ . There is no maximum over the given constraints.

7 0

3 years ago

John is 3 years younger than twice Monica's age. If m represents Monica's age, which equation can be used to find j, John's age?

AnnZ [28]

Answer:

J =2m -3

Step-by-step explanation:

2m is twice Monica's age

-3 represents 3 years younger

7 0

2 years ago

Y varies inversely with x<br> k= 1.25<br> What is the value of y when x is 5?

alexgriva [62]

Answer:

The value of y is 0.25

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form $y*x=k$ or $y=k/x$

For x=5

Find the value of y

k=1.25

substitute in the equation

$y=k/x$ -----> $y=1.25/5=0.25$

4 0

3 years ago

A computer company's stock costs $122 at the start of the day. At the end of the day it costs $93. By what amount did the stock'

Helga [31]

Answer:

the amount the stock changed over the day = $29

Step-by-step explanation:

The stock cost $122 at the start of the day . At the end of the day it cost $93. The amount the stock value changed can be calculated below.

The initial amount of the stock that days was $122 but at the end of the day it changes to $93. This means the stock cost decreases over the day.

Initial cost of stock at the day = $122

Final cost at the end of the day = $93

the amount the stock changes over the day = initial cost of stock at the day - final cost at the end of the day.

the amount the stock changes over the day = 122 - 93

the amount the stock changed over the day = $29

Generally, the stock decreased over the day.

7 0

3 years ago

The gym teacher is setting up for a field

irinina [24]

$630

The total perimeter is 42 and 42x15=630

7 0

2 years ago