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Natasha2012 [34]

3 years ago

8

Which ordered pair is a solution to the following

1 answer:

Jet001 [13]3 years ago

3 0

Answer:

A.

If you graph them, the answer A will be inside of the shaded area.

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X – 10x = 100

kenny6666 [7]

Answer:

-11.01 or -11

Step-by-step explanation:

x-10x=100

1x-10x=100

-9x = 100

-9x/-9 =100/-9

x = -11.01

No calculator used

8 0

3 years ago

The equations that must be solved for maximum or minimum values of a differentiable function w=f(x,y,z) subject to two constrai

sammy [17]

The Lagrangian is

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

with partial derivatives (set equal to 0)

$L_x=2x+8\lambda x+2\mu=0\implies x(1+4\lambda)+\mu=0$

$L_y=2y+8\lambda y=0\implies y(1+4\lambda)=0$

$L_z=2z-2\lambda z+4\mu=0\implies z(1-\lambda)+2\mu=0$

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

$L_\mu=2x+4z-2=0\implies x+2z=1$

Case 1: If $y=0$ , then

$4x^2-z^2=0\implies4x^2=z^2\implies2|x|=|z|$

Then

$x+2z=1\implies x=1-2z\implies2|1-2z|=|z|\implies z=\dfrac25\text{ or }z=\dfrac23$

$\implies x=\dfrac15\text{ or }x=-\dfrac13$

So we have two critical points, $\left(\dfrac15,0,\dfrac25\right)$ and $\left(-\dfrac13,0,\dfrac23\right)$

Case 2: If $\lambda=-\dfrac14$ , then in the first equation we get

$x(1+4\lambda)+\mu=\mu=0$

and from the third equation,

$z(1-\lambda)+2\mu=\dfrac54z=0\implies z=0$

Then

$x+2z=1\implies x=1$

$4x^2+4y^2-z^2=0\implies1+y^2=0$

but there are no real solutions for $y$ , so this case yields no additional critical points.

So at the two critical points we've found, we get extreme values of

$f\left(\dfrac15,0,\dfrac25\right)=\dfrac15$ (min)

and

$f\left(-\dfrac13,0,\dfrac23\right)=\dfrac59$ (max)

5 0

4 years ago

In which type of triangle is the othocenter on the perimeter of the triangle?

Snezhnost [94]

Answer:

A right triangle

Step-by-step explanation:

It's where the altitudes all intersect. In a right triangle, the legs of the right triangle are the altitudes-- especially evident when the right angle is at the base. The altitude from the hypotenuse to the right angle also passes through the right angle.

8 0

4 years ago

Simplify 1/3(9a + b) - 1/2(4a + 2b).

MAVERICK [17]

Use distributive property: a(b + c) = ab + ac

1/3(9a + b) - 1/2(4a + 2b) = 3a + 1/3b - 2a - b = a - 2/3b

6 0

4 years ago

Will Give Brainliest

Katarina [22]

Answer:

4/6

Step-by-step explanation:

im smart trust

5 0

3 years ago