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3 years ago

WILL GIVE BRAINLIEST!!

Mathematics

1 answer:

Molodets [167]3 years ago

7 0

The first option is correct because it's far from the rest of the data
Second is correct too because several dots are in that area
3 and 4 are not true

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Leandro wants to build a one-sample

9966 [12]

Answer:

2.326

Step-by-step explanation:

3 0

3 years ago

Find the maximum and minimum values attained by f(x, y, z) = 5xyz on the unit ball x2 + y2 + z2 ≤ 1.

Allushta [10]

Check for critical points within the unit ball by solving for when the first-order partial derivatives vanish:
$f_x=5yz=0\implies y=0\text{ or }z=0$
$f_y=5xz=0\implies x=0\text{ or }z=0$
$f_z=5xy=0\implies x=0\text{ or }y=0$

Taken together, we find that (0, 0, 0) appears to be the only critical point on $f$ within the ball. At this point, we have $f(0,0,0)=0$ .

Now let's use the method of Lagrange multipliers to look for critical points on the boundary. We have the Lagrangian

$L(x,y,z,\lambda)=5xyz+\lambda(x^2+y^2+z^2-1)$

with partial derivatives (set to 0)

$L_x=5yz+2\lambda x=0$
$L_y=5xz+2\lambda y=0$
$L_z=5xy+2\lambda z=0$
$L_\lambda=x^2+y^2+z^2-1=0$

We then observe that

$xL_x+yL_y+zL_z=0\implies15xyz+2\lambda=0\implies\lambda=-\dfrac{15xyz}2$

So, ignoring the critical point we've already found at (0, 0, 0),

$5yz+2\left(-\dfrac{15xyz}2\right)x=0\implies5yz(1-3x^2)=0\implies x=\pm\dfrac1{\sqrt3}$
$5xz+2\left(-\dfrac{15xyz}2\right)y=0\implies5xz(1-3y^2)=0\implies y=\pm\dfrac1{\sqrt3}$
$5xy+2\left(-\dfrac{15xyz}2\right)z=0\implies5xy(1-3z^2)=0\implies z=\pm\dfrac1{\sqrt3}$

So ultimately, we have 9 critical points - 1 at the origin (0, 0, 0), and 8 at the various combinations of $\left(\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3}\right)$ , at which points we get a value of either of $\pm\dfrac5{\sqrt3}$ , with the maximum being the positive value and the minimum being the negative one.

5 0

3 years ago

What is the value of x in the equation 2x - 3 = 9- 4x? o 6 o 3 O 1 02

riadik2000 [5.3K]

Answer:

2? The last one

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

HERE IS THE ONE WITH THE QUESTION LOL PLZ ANSWER

ZanzabumX [31]

Answer:

The graph goes with the third chart

Step-by-step explanation:

Y starts at 3 and then goes up to 4,5, and then 6 while x starts at 0 and goes up to 1,2, and 3

8 0

2 years ago

a survey of factories in five northeastern states found that 10% of the 300 workers surveyed were satisfied with the benefits of

DiKsa [7]

Well I don't know if i'm answering the question, but 30 workers surveyed were satisfied with the benefits they received from the employers because 300 multiplied by .10 is 30. Hope my answer is useful.

5 0

3 years ago