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aleksandrvk [35]
3 years ago
10

Please help me branniest

Mathematics
1 answer:
maxonik [38]3 years ago
5 0
The answer is option A

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10 POINTS answer ASAP if you can
Dafna1 [17]

Answer:

I think it is

Step-by-step explanation:

t

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You have already saved $55. You can earn $9 per hour at your job. You are saving for a bicycle that costs $199. What inequality
Sveta_85 [38]

y = 9x + 55 because the 9x is the amount you get paid an hour, and to get to the 199 you need to include to rate at which you get paid, and add that to how much you already have saved.

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3 years ago
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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
WORTH 25 POINTS AND WILL MARK BRANLIEST Write an expression that can be used to determine the final cost of the cards. ThE ANSWE
vlada-n [284]

Answer: ...

Step-by-step explanation: I will rather let you use a variable and solve (for example: x!

6 0
3 years ago
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A botanist transplanted a plant that
KengaRu [80]

Linear equation of plant height is h = (1/2)w + 3

Given:

Height of experimental plant = 3cm

Average growth = 0.5 cm per week

Find:

Linear equation of plant height

Computation:

Given;

h = Plant height

w = number of weeks

So,

Plant height = Height of experimental plant + (Average growth)(number of weeks)

h = 3 + (0.5)(w)

h = (1/2)w + 3

Option "J" is the correct answer to the following question.

Learn more:

brainly.com/question/14342708?referrer=searchResults

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