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2 years ago

Question in picture. ty

Mathematics

1 answer:

sleet_krkn [62]2 years ago

5 0

Answer:

input x = - 7

Step-by-step explanation:

A is modelled as y = 5x - 4

B is modelled as y = 3x + 8

We require output of A three times the output of B , then

5x - 4 = 3(3x + 8) ← distribute

5x - 4 = 9x + 24 ( subtract 9x from both sides )

- 4x - 4 = 24 ( add 4 to both sides )

- 4x = 28 ( divide both sides by - 4 )

x = - 7 ← input

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Use Lagrange multipliers to find the maximum and minimum values of

marusya05 [52]

The Lagrangian is

$L(x,y,\lambda)=x+8y+\lambda(x^2+y^2-4)$

It has critical points where the first order derivatives vanish:

$L_x=1+2\lambda x=0\implies\lambda=-\dfrac1{2x}$

$L_y=8+2\lambda y=0\implies\lambda=-\dfrac4y$

$L_\lambda=x^2+y^2-4=0$

From the first two equations we get

$-\dfrac1{2x}=-\dfrac4y\implies y=8x$

Then

$x^2+y^2=65x^2=4\implies x=\pm\dfrac2{\sqrt{65}}\implies y=\pm\dfrac{16}{\sqrt{65}}$

At these critical points, we have

$f\left(\dfrac2{\sqrt{65}},\dfrac{16}{\sqrt{65}}\right)=2\sqrt{65}\approx16.125$ (maximum)

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3 years ago

What is the approximate area of a regular heptagon with a side length of 4 inches and a distance from the center to a vertex of

jok3333 [9.3K]

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2 years ago

In the probability distribution to the right, the random variable X represents the number of marriages an individual aged 15 ye

kodGreya [7K]

The table of the probability is missing, so i have attached it.

Answer:

μ = 0.919

The interpretation of this is that;on the average, an individual aged 15 years or older has been involved in 0.919 marriages.

Step-by-step explanation:

The expected value which is also called mean value is denoted by the symbol μ. It is defined as the sum of the product of each possibility x with it's probability P(x) as the formula;

μ = Σx.P(x) = (0 × 0.272) + (1 × 0.575) + (2 × 0.121) + (3 × 0.027) + (4 × 0.004) + (5 × 0.001)

μ = 0.919

Thus, the interpretation of this is that;on the average, an individual aged 15 years or older has been involved in 0.919 marriages.