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Iteru [2.4K]
3 years ago
9

Use the method of Lagrange Multipliers to find any maximum or minimum values of the function f(x,y)=x2+y2 subject to the constra

int xy=1.

Mathematics
1 answer:
Sphinxa [80]3 years ago
3 0

Answer:

possible maximum and minimum values : f (1,1),  f (-1,-1)

Step-by-step explanation:

Given function :

f(x,y) = x^2 + y^2

constraint = xy = 1

attached below is the detailed solution of the method of using Lagrange method of Multipliers  to find the maximum and minimum values of the function

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Write the expression 44(4–7)(4) using a single exponent.
Ghella [55]
<h3>The given expression as single exponent is:</h3>

4^4 \times 4^{-7} \times 4 = 4^{-2}

<em><u>Solution:</u></em>

<em><u>Given expression is:</u></em>

4^4 \times 4^{-7} \times 4

In exponents,

When the base is same, exponents can be added

Which means,

a^m \times a^n = a^{m+n}

Therefore,

4^4 \times 4^{-7} \times 4 = 4^{4-7+1}\\\\Simplify\\\\4^4 \times 4^{-7} \times 4 = 4^{-3+1} \\\\4^4 \times 4^{-7} \times 4 = 4^{-2}

Thus the given expression as single exponent is:

4^4 \times 4^{-7} \times 4 = 4^{-2}

8 0
3 years ago
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Jayden had $8 last week. He now has $11. What is the percent of change?
vagabundo [1.1K]

Answer:

37.5 %

Step-by-step explanation:

11/8 = 1.375

1.375 x 100 = 137.5 %

137.5% - 100% = 37.5%

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Help please I’ll mark u brilliant
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The answer should be (x, y) —> (x - 8, y + 10)
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The probability of drawing a pearl bead out of a bag of mixed beads is 2/3. What is the probability of drawing a bead which is n
tatiyna

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the probability is 1/3

Step-by-step explanation:

6 0
3 years ago
Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for aluminum alloy sheets of a parti
Marizza181 [45]

Answer:

a) X^ = 70 GPa , s = 0.4 GPa

b) X^ = 70 GPa , s = 0.2 GPa

c) n = 64 .. part b

Step-by-step explanation:

Solution:-

- A sample ( n ) was taken from aluminum alloy sheets of a particular type the distribution parameters are given below:

                      Mean ( u ) = 70 GPa

                      Standard deviation ( σ ) = 1.6 GPa

a)

- We take a sample size of n = 16. The random variable X denotes the distribution of the sample obtained.

- We will estimate the parameters of the sample distribution X.

- The point estimate method tells us that the population mean ( u ) is assumed as the sample mean ( X^ ).

                    Sample Mean ( X^ ) = u = 70 GPa

- The sample standard deviation ( s ) for the given sample with known population standard deviation ( σ ) is given by:

                   sample standard deviation ( s ) = σ / √n

                   sample standard deviation ( s ) = 1.6 / √16

                   sample standard deviation ( s ) = 0.4 GPa

b)

Repeat the above calculations for sample size n =  64.

- We will estimate the parameters of the sample distribution X.

- The point estimate method tells us that the population mean ( u ) is assumed as the sample mean ( X^ ).

                    Sample Mean ( X^ ) = u = 70 GPa

- The sample standard deviation ( s ) for the given sample with known population standard deviation ( σ ) is given by:

                   sample standard deviation ( s ) = σ / √n

                   sample standard deviation ( s ) = 1.6 / √64

                   sample standard deviation ( s ) = 0.2 GPa

c)

- The standard deviation ( s ) gives us the uncertainty of mean ( X^ ). How spread apart/close are the data points from the mean.

- We see that standard deviation ( s ) has an inverse relation to the sample size ( n ):

                   sample standard deviation ( s ) = σ / √n

- So with increasing sample size the there is a decreased variability in the sample distribution of ( X ).

Answer: The sample size n = 64 used in part b would give us lesser variability of sample distribution of X as compared to sample size n = 16 used in part a. Hence, X is more likely to be within 1 GPa of the mean in part (b). This is due to the decreased variability

4 0
3 years ago
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