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3 years ago

13

Kayla and Jody are working at a station. They have been given four cards with four different functions on them.

1 answer:

aniked [119]3 years ago

6 0

If x=0, then f(x)=-1. The value of -1 makes Function D less than any of the other functions.
f(0)=2(0^2)-1
=2(0)-1
=0-1
=-1

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Find the absolute maximum and minimum values of the following functions on the given curves functions:

bagirrra123 [75]

Answer:

Solution has explained below:

Step-by-step explanation:

(a) f(x,y) = x+y

To find out the maximum and minimum values, we need to find first and second derivatives, we have

fx= 1, fx₁=0 and

fy= 1 and fyy=0

For stationary points fx=fy=0, which gives,

1=1=0, so that there is just one stationary point, (x,y)=(0,0)

If fx₁ < 0 and fyy < 0, function is maximum

If fx₁ > 0 and fyy > 0, function is minimum.

(b) g(x,y) = xy

Sol: To find out the maximum and minimum values, we need to find first and second derivatives, we have

fx= 1 and fy = 1

fx₁ = 0 and fyy =0

for stationary points fx = fy =0, which gives 1=1=0, so that there is just one stationary points, (x,y) =(0,0)

If fx₁ < 0 and fyy < 0, function is maximum.

If fx₁ > 0 and fyy> 0, function is minimum.

c) h(x,y) = 2x2 + y2

sol: To find out the maximum and minimum values, we need to find first and second derivatives, we have

fx = 4x and fy = 2y

fx₁= 4 and fyy = 2

Now, taking fx = 0 and fy = 0

Gives x=0 and y=0,

Stationary points are (x,y) = (0,0)

If fx₁ < 0 and fyy < 0, solution is maximum,

If fx₁ > 0 and fyy > 0, solution is minimum,

Here, fx₁ = 4 > 0 and fyy = 2 > 0.

6 0

3 years ago

Linar system in variables<br> -x-3y-2z=8,<br> -x+y+6z=, <br> x-9y-2z=4

docker41 [41]

Answer:

-x+y+6z=? You did not spcify so I just made it 0

x = -22/5, y = -4/5, z = -3/5

Step-by-step explanation:

Solve the following system:

{-x - 3 y - 2 z = 8 | (equation 1)

-x + y + 6 z = 0 | (equation 2)

x - 9 y - 2 z = 4 | (equation 3)

Subtract equation 1 from equation 2:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+4 y + 8 z = -8 | (equation 2)

x - 9 y - 2 z = 4 | (equation 3)

Divide equation 2 by 4:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y + 2 z = -2 | (equation 2)

x - 9 y - 2 z = 4 | (equation 3)

Add equation 1 to equation 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y + 2 z = -2 | (equation 2)

0 x - 12 y - 4 z = 12 | (equation 3)

Divide equation 3 by 4:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y + 2 z = -2 | (equation 2)

0 x - 3 y - z = 3 | (equation 3)

Swap equation 2 with equation 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+y + 2 z = -2 | (equation 3)

Add 1/3 × (equation 2) to equation 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+0 y+(5 z)/3 = -1 | (equation 3)

Multiply equation 3 by 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+0 y+5 z = -3 | (equation 3)

Divide equation 3 by 5:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Add equation 3 to equation 2:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y+0 z = 12/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Divide equation 2 by -3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Add 3 × (equation 2) to equation 1:

{-x + 0 y - 2 z = 28/5 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Add 2 × (equation 3) to equation 1:

{-x+0 y+0 z = 22/5 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Multiply equation 1 by -1:

{x+0 y+0 z = -22/5 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Collect results:

Answer: {x = -22/5, y = -4/5, z = -3/5

8 0

3 years ago

51 divided by 3 is k.<br> Solve for k.<br> k<br> =

SVETLANKA909090 [29]

17 ... 51 divided by 3 is 17

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vredina [299]

Answer:

g = h(e-10)

Step-by-step explanation:

You can multiply the whole equation by h to get g by itself.

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Step-by-step explanation:

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