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anzhelika [568]

3 years ago

14

Vertex of y=5x^2-10x+1

1 answer:

kirill [66]3 years ago

4 0

Convert to vertex form:-

y = 5(x^2 - 2x) + 1

y = 5[(x - 1)^2 - 1] + 1

y = 5(x - 1)^2 - 4

vertex is (1, -4)

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EXAMPLE 5 Find the maximum value of the function f(x, y, z) = x + 2y + 9z on the curve of intersection of the plane x − y + z =

geniusboy [140]

The Lagrangian,

$L(x,y,z,\lambda,\mu)=x+2y+9z-\lambda(x-y+z-1)-\mu(x^2+y^2-1)$

has critical points where its partial derivatives vanish:

$L_x=1-\lambda-2\mu x=0$

$L_y=2+\lambda-2\mu y=0$

$L_z=9-\lambda=0$

$L_\lambda=x-y+z-1=0$

$L_\mu=x^2+y^2-1=0$

$L_z=0$ tells us $\lambda=9$ , so that

$L_x=0\implies-8-2\mu x=0\implies x=-\dfrac4\mu$

$L_y=0\implies11-2\mu y=0\implies y=\dfrac{11}{2\mu}$

Then with $L_\mu=0$ , we get

$x^2+y^2=\dfrac{16}{\mu^2}+\dfrac{121}{4\mu^2}=1\implies\mu=\pm\dfrac{\sqrt{185}}2$

and $L_\lambda=0$ tells us

$x-y+z=-\dfrac4\mu-\dfrac{11}{2\mu}+z=1\implies z=1+\dfrac{19}{2\mu}$

Then there are two critical points, $\left(\pm\frac8{\sqrt{185}},\mp\frac{11}{\sqrt{185}},1\pm\frac{19}{\sqrt{185}}\right)$ . The critical point with the negative $x$ -coordinates gives the maximum value, $9+\sqrt{185}$ .

8 0

4 years ago

What is the greatest common factor of 12хуб + 60xy? — 24x°у? ?

Liula [17]

The greatest common factor is $12xy$

Explanation:

The given expression is $12xy^6+60xy$

We need to determine the greatest common factor of the given expression.

The greatest common factor of two numbers is the largest number of the two numbers that divides them both.

Hence, from the given expression, let us common out the highest factor that divides the two numbers.

Thus, we have,

$12xy^6+60xy=12xy(y^5+5y)$

Thus, the largest number that divides both the terms is $12xy$

Hence, the greatest common factor of the given expression is $12xy$

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yuradex [85]

Answer: 106 and 195/256

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abio and Carlos play on a basketball team together. In the last game, Fabio had 777 points less than 222 times as many points as

tankabanditka [31]

Answer:

The equation 31=2c-7 to determine the number of points Carlos scored in the last game.

Step-by-step explanation:

We are given with,(I think every number is repeating for 3 times. So, I took each number as once)

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Let Carlos scored in the last game as "C".

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31= 2c-7

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tino4ka555 [31]

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Step-by-step explanation:

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3 years ago

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