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Kitty [74]
3 years ago
11

What is 8g-6(g+1)<4(2g-9)

Mathematics
1 answer:
Alex3 years ago
8 0

Answer:

5 < g

Step-by-step explanation:

8g -6(g + 1) < 4(2g - 9)

8g -6g - 6 < 8g - 36

2g - 6 < 8g - 36

30 < 6g

5 < g

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Sav [38]
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8 0
3 years ago
Use the method of lagrange multipliers to find
Yanka [14]

Answer:

a) The function is: f(x, y) = x + y.

The constraint is: x*y = 196.

Remember that we must write the constraint as:

g(x, y) = x*y - 196 = 0

Then we have:

L(x, y, λ) = f(x, y) +  λ*g(x, y)

L(x, y,  λ) = x + y +  λ*(x*y - 196)

Now, let's compute the partial derivations, those must be zero.

dL/dx =  λ*y + 1

dL/dy =  λ*x + 1

dL/dλ = (x*y - 196)

Those must be equal to zero, then we have a system of equations:

λ*y + 1 = 0

λ*x + 1 = 0

(x*y - 196) = 0

Let's solve this, in the first equation we can isolate  λ to get:

λ = -1/y

Now we can replace this in the second equation and get;

-x/y + 1 = 0

Now let's isolate x.

x = y

Now we can replace this in the last equation, and we will get:

(x*x - 196) = 0

x^2 = 196

x = √196 = 14

then the minimum will be:

x + y = x + x = 14 + 14 = 28.

b) Now we have:

f(x) = x*y

g(x) = x + y - 196

Let's do the same as before:

L(x, y, λ) = f(x, y) +  λ*g(x, y)

L(x, y, λ) = x*y +  λ*(x + y - 196)

Now let's do the derivations:

dL/dx = y + λ

dL/dy = x + λ

dL/dλ = x + y - 196

Now we have the system of equations:

y + λ = 0

x + λ = 0

x + y - 196 = 0

To solve it, we can isolate lambda in the first equation to get:

λ = -y

Now we can replace this in the second equation:

x - y = 0

Now we can isolate x:

x = y

now we can replace that in the last equation

y + y - 196 = 0

2*y - 196 = 0

2*y = 196

y = 196/2 = 98

The maximum will be:

x*y = y*y = 98*98 = 9,604

6 0
3 years ago
Which of the following are examples of irrational numbers?
andreyandreev [35.5K]
√4 + √16 = 2 + 4 = 6   <--- rational
√5 + √36 = √5 + 6   <--- irrational 
√9 + √24 = 3 + √24   <--- irrational
2 * √4 = 2 * 2 = 4   <--- rational 
√49 * √81 = 7 * 9 = 63   <---rational
3√12 = 3√(4 * 3) = (3 * 2)√3 = 6√3    <---irrational

Hope this helps ^-^
5 0
3 years ago
Read 2 more answers
Look at the table below. Plot and label points M and N on the coordinate
marta [7]
M = (1,4)
N = (5,2)

For M, you simply move to 1 on the x axis abs for 4 you move on the y axis. Same does for N, for 5 you move on the x axis and for 2 you move on the y axis.
6 0
3 years ago
enrollment in the ski/snowboard club increased by 30% this year. there are now 182 students in the club. how many students were
eduard
Enrolement increased by 30% that means last year=100%
incease of 30%=30+100=130% now

now=182

percent means parts out of 100 so
130%=130/100=13/10


182=13/10 of x (x represents the number last year)
of means multipy so
182=13/10 times x
multiply both sides by 10/13 to clear fraction
182 times 10/13=x=140



140 students last year
8 0
3 years ago
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