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Goryan [66]
2 years ago
8

Help pls What is the solution to this system of equations? x = 12 − y 2x + 3y = 29

Mathematics
1 answer:
Oxana [17]2 years ago
3 0

Answer:

       

Step-by-step explanation:

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Find all points on the portion of the plane x+y+z=5 in the first octant at which f(x, y, z) = xy2z2 has a maximum value.
irina1246 [14]
Lagrange multipliers:

L(x,y,z,\lambda)=xy^2z^2+\lambda(x+y+z-5)

L_x=y^2z^2+\lambda=0
L_y=2xyz^2+\lambda=0
L_z=2xy^2z+\lambda=0
L_\lambda=x+y+z-5=0

\lambda=-y^2z^2=-2xyz^2=-2xy^2z

-y^2z^2=-2xyz^2\implies y=2x (if y,z\neq0)

-y^2z^2=-2xy^2z\implies z=2x (if y,z\neq0)

-2xyz^2=-2xy^2z\implies z=y (if x,y,z\neq0)

In the first octant, we assume x,y,z>0, so we can ignore the caveats above. Now,

x+y+z=5\iff x+2x+2x=5x=5\implies x=1\implies y=z=2

so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of f(1,2,2)=16.

We also need to check the boundary of the region, i.e. the intersection of x+y+z=5 with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force f(x,y,z)=0, so the point we found is the only extremum.
4 0
3 years ago
Can someone help me with this question please and thank you.
Diano4ka-milaya [45]
Is there a graph or chart? Or a word problem that tells us some information
4 0
3 years ago
Evaluate 6²-7²+8²-9²+..+998²-999²​
Llana [10]

Answer:

-499,485.

Step-by-step explanation:

We can transform this to an arithmetic series by  working it out in pairs:

6^2 - 7^2 = (6-7)(6+7) = -13

8^2 - 9^2 = (8-9)*8+9) = -17  

10^2 - 11^2 = -1 * 21 = -21 and so on

The common difference is -4.

The number of terms in this series  is (998 - 6) / 2 + 1

= 992/2 + 1 = 497.

Sum of n terms of an A.S:

= n/2 [2a1 + (n - 1)d  

Here a1 = -13, n = 497, d = -4:

Sum = (497/2)[-26 - 4(497-1)]

= 497/2 * -2010

= -499,485.

3 0
3 years ago
Bobby’s uncle gave him 300 baseball cards. Each week, Bobby purchases 40 baseball cards to add to his collection.
Julli [10]

Answer:

C

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Please help me with this question please!!!
lozanna [386]

A = x * x = x^2

B = 6 * x = 6x

C = 8 * x = 8x

D = 6 * 8 = 48

So the area of the whole shape is each side added up then multiplied to give (x+6)(x+8) =

x^2 + 14x + 48

7 0
3 years ago
Read 2 more answers
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