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user100 [1]
3 years ago
10

Graph the system of equations on your graph paper to answer the question

Mathematics
1 answer:
UNO [17]3 years ago
7 0

Since we have to solve this system graphically, we'll have to draw both lines.

To draw a line, simply build a little tables with two x,y values: for the first line we have

\begin{array}{c|c}x&-x+3\\0&3\\1&2\end{array}

So, you can draw the points (0,3) and (1,2), connect them, and you'll have the graph of the line y=-x+3

For the second line we have

\begin{array}{c|c}x&x+5\\0&5\\1&6\end{array}

So, you can draw the points (0,5) and (1,6), connect them, and you'll have the graph of the line y=x+5

Finally, we have to check where the two lines cross. If your drawing is accurate enough, you'll see that the point you're looking for is (-1, 4)

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Find the local maximum and minimum values and saddle point(s) of the function.
iogann1982 [59]
f(x,y)=9e^y(y^2-x^2)
\nabla f=\left\langle-18xe^y,9ye^y(2+y)\right\rangle

Critical points occur where the gradient is zero. This is guaranteed whenever x=0 and either y=0 or y=-2.

The Hessian matrix for this function looks like

H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}-18e^y&-18xe^y\\-18xe^y&9e^y(2-x^2+4y+y^2)\end{bmatrix}

and has determinant

|H(x,y)|=-162e^{2y}(2+x^2+4y+y^2)

Maxima occur whenever the determinant is positive and f_{xx}. Minima occur whenever both the determinant and f_{xx} are positive. Saddle points occur whenever the determinant is negative.

At (0,0), you have a saddle point since the determinant reduces to -324, so (0,0,0) is the saddle point.

At (0,-2), the determinant is \dfrac{324}{e^4}>0 and f_{xx}(0,-2)=-\dfrac{18}{e^2}, so \left(0,-2,\dfrac{36}{e^2}\right) is a local maximum.

No other critical points remain, so you're done.
4 0
3 years ago
Which method is used in elimination to find the solutions of x + 3y = 9 and x - 3y = 8?
weqwewe [10]

Answer:

x=17/2  y=1/6

Step-by-step explanation:

-1(x+3y=9)

1(x-3y=8)

_________

-x-3y=-9

x-3y=8

________

-6y/6=-1/6   y=1/6

x+3(1/6)=9

x+ 1/2=9

   - 1/2  - 1/2

x=17/2

4 0
3 years ago
ITS AN EMERGENCY PLEASE!
Lady bird [3.3K]
I’m pretty sure the power is 4
3 0
3 years ago
Connie is packing for a trip. She has 17 pairs of jeans. If she has room to pack 6 pairs how many ways can she choose which jean
Evgesh-ka [11]

Answer:12,376

Step-by-step explanation:

Given

Connie has 17 Pairs of jeans

She has to choose 6 pairs out of 17

We know, no of ways to pick r items out of n items is ^nC_r

\therefore \text{No of ways is =}^{17}C_6\\\\\Rightarrow \dfrac{17!}{(17-6)!6!}=12,376\ \text{ways}

6 0
3 years ago
36 is _______% less than 60?<br><br> 24%<br><br><br> 40%<br><br><br> 60%<br><br><br> 67%
ioda
40%less You take 36/60 That equals 60% This means that 36 is 60% of 60 So in 24 is 40% of 60 or 36 is 40% less than 60
3 0
3 years ago
Read 2 more answers
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