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4 years ago

5

Arianna correctly simplified an expression. When she substituted x=2into the simplified expression, the value was –4. Which coul

d be Arianna’s original expression?

2 answers:

Nata [24]4 years ago

7 0

$x - 6$
$= - 4$

liberstina [14]4 years ago

6 0

Answer:

$\frac{1}{6}(-10x-4)$

Step-by-step explanation:

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The plane x + y + 2z = 12 intersects the paraboloid z = x2 + y2 in an ellipse. Find the points on the ellipse that are nearest t

Soloha48 [4]

The distance between a point $(x,y,z)$ and the origin is $\sqrt{x^2+y^2+z^2}$ . But since $(\sqrt{f(x)})'=\frac{f'(x)}{2\sqrt{f(x)}}$ , both $f(x)$ and $\sqrt{f(x)}$ have the same critical points, so we can consider instead the squared distance, $x^2+y^2+z^2$ .

We're looking for the extrema of $x^2+y^2+z^2$ subject to $x+y+2z=12$ and $z=x^2+y^2$ . The Lagrangian is

$L(x,y,z,\lambda,\mu)=x^2+y^2+z^2+\lambda(x+y+2z-12)+\mu(z-x^2-y^2)$

with critical points where the partial derivatives vanish:

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

$L_y=2y+\lambda-2\mu y=0\implies\lambda=2y(\mu-1)$

$L_z=2z+2\lambda+\mu=0$

$L_\lambda=x+y+2z-12=0$

$L_\mu=z-x^2-y^2=0$

From the first two equations, it follows that $x=y$ .

Then in the last two equations,

$x+y+2z-12=0\implies x+z=6$

$z-x^2-y^2=0\implies z=2x^2$

$\implies x+2x^2=6\implies2x^2+x-6=(2x-3)(x+2)=0\implies x=\dfrac32\text{ or }x=-2$

If $x=\frac32$ , then $z=6-\frac32=\frac92$ ; if $x=-2$ , then $z=8$ .

So there are two critical points, $\left(\frac32,\frac32,\frac92\right)$ and $(-2,-2,8)$ .

Let $f(x,y,z)=\sqrt{x^2+y^2+z^2}$ . We have a minimum distance of $f\left(\frac32,\frac32,\frac92\right)=\boxed{\frac{3\sqrt{11}}2}$ and maximum distance of $f(-2,-2,8)=\boxed{6\sqrt2}$ .

8 0

4 years ago

Points points points

GrogVix [38]

The answer would be C. What you will do is use the Midpoint formula. (x1+x2/2, y1+y2/2).
Hope this helps! (:

5 0

3 years ago

Read 2 more answers

Write the equation of the line

meriva

Answer:

gradient is the same as slope

so m=9

Step-by-step explanation:

y=9x+C. insert point(1,4)

4=9*1+C

4-9=C

C=-5

so the equation of the line is y=9x-5

7 0

3 years ago

Read 2 more answers

What is the area of this figure?

Alborosie

Answer:

146

Step-by-step explanation:

Hey there to find the area of this shape we will divide it into 2 shapes first one is a trapezoid and the second one is a triangle. first, we find the area of a trapezoid. to find the area of a trapezoid we use the formula:

A = $\frac{a+b}{2} * h$

in this situation

a = 4

b = 14

h = 10

Now we plug it into the formula which will look like:

A = $\frac{4+14}{2}*10$

if we solve it:

4+14 = 18

18/2 = 9

9*10 = 90

so the area of the trapezoid is 90

Now we find the area of triangle. to find the area of a triangle we use the formula:

A = $\frac{1}{2} * b * h$

in this situation

b = 14

h = 8 ( because the height of the trapezoid was 10 and the height of both shapes combined is 18 so we do 18 - 10 = 8 )

Now we put the numbers into the formula which will look like:

A = $\frac{1}{2}*14*8$

if we solve it :

14*8 = 112

$112*\frac{1}{2}$ = 56

so the area of the triangle is 56

Now we add the area of both shapes:

56 + 90 = 146

area of the big shape = 146

Have a wonderful day

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3 years ago

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What is three ways you can find the area of a rectangle

boyakko [2]

Answer:

here's one l times height idk the other two lol

Step-by-step explanation:sorry

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3 years ago