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Lesechka [4]
3 years ago
13

What is side by side by side similarity theorem?

Mathematics
1 answer:
Licemer1 [7]3 years ago
3 0
Side ang side similaruty
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What is the domain and range of y=6?
grigory [225]
The domain should be
 (-∞, ∞) {y|y ∈ R}
<span>And the range is:
{6}
</span>
8 0
3 years ago
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Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. f(x, y) = 2x2y,
hjlf

Answer:

f(-2,-1) = -8 is the minimum value of f(x,y)

f(2,1) = 8 is the maximum value of f(x,y)

Step-by-step explanation:

f(x,y) = 2x²y under the constraint 2x² + 4y² = 12

Let g(x,y) = 2x² + 4y² - 12

df/dx = 4xy, df/dy = 2x², dg/dx = 4x and dg/dy = 8y

Now, using the principle of Lagrange multipliers,

df/dx + λdg/dx = 0 and df/dy + λdg/dy = 0.

Substituting the values of the variables, we have

df/dx + λdg/dx = 0    and df/dy + λdg/dy = 0.

4xy + 4xλ = 0      (1)           2x² + 8λy = 0  (2)

xy + xλ = 0

x(y + λ) = 0

x = 0 or y + λ = 0

Since x ≠ 0, y = -λ

Substituting y = -λ into (2), we have

2x² + 8λy = 0

2x² + 8λ(-λ) = 0

2x² - 8λ² = 0

2x² = 8λ²

x² = 4λ²

x = ±2λ  

Substituting the values of x and y into the constraint equation, we have

2x² + 4y² = 12

2(±2λ)² + 4(-λ)² = 12

2(4)λ² + 4λ² = 12

8λ² + 4λ² = 12

12λ² = 12

λ² = 1

λ = ±1

Substituting the value of  λ into x and y, we have

x = ±2λ = ±2(±1) = ±2

y = -λ = -(±1) = ±1

The minimum values of x and y are -2 and -1 respectively. Substituting these int f(x,y), we have

f(-2,-1) = 2(-2)²(-1) = 2 × 4 × (-1) = -8

So f(-2,-1) = -8 is the minimum value of f(x,y)

The maximum values of x and y are 2 and 1 respectively. Substituting these int f(x,y), we have

f(2,1) = 2(2)²(1) = 2 × 4 × 1 = 8

So f(2,1) = 8 is the maximum value of f(x,y)

7 0
3 years ago
-7 + 2x = -45<br> a 1<br> b -19<br> c 11<br> d -16
Marina86 [1]

Answer:

B) -19

Step-by-step explanation:

-7 + 2x = -45

+7             +7

2x = -38

/2      /2

x = -19

7 0
3 years ago
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It is important to know the appropriate dose of ibuprofen for a child so that you are ready in the case of high fever. The dosin
Alexus [3.1K]

Answer:

102 mg

Step-by-step explanation:

Let's convert 28 pounds to kgs.

Since 1 kg = 2.2 pounds, we can find:

\frac{1Kg}{2.2Pounds}=\frac{xKg}{28Pounds}\\1*28=2.2x\\28=2.2x\\x=\frac{28}{2.2}\\x=12.73

So 28 pounds is 12.73 Kg

Since 8mg is given per kg, for 12.73 kg, the amount given should be:

12.73 * 8 = 101.84

Rounded to nearest whole number, that is, 102 mg

8 0
3 years ago
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A lighthouse has a shadow that is 36 feet long.
VLD [36.1K]
To find this it would be 36/3=4/x
Then cross multiply
36*4/3
That’s the answer
5 0
3 years ago
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