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3 years ago

List these least to greather 5,-2,-1,4

Mathematics

1 answer:

zhenek [66]3 years ago

8 0

This will be from least to greater -1 -2 4 5

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How do I solve this?

bulgar [2K]

Answer:

I think you should try the method of substitution???

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3 years ago

Question 9 of 10 Which of the following is most likely the next step in the series? OA. O B. O C. O D.

uranmaximum [27]

Answer:

Step-by-step explanation:

Vertical line is removed then horizontal. Its goes blue, red, blue. A vertical line is to be removed and the colour is red. That leaves B as the answer.

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3 years ago

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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.

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3 years ago

Ellie drives 22.5 miles in 45 minutes. If she drove three hours in total at the same rate, how far did she go?

Scilla [17]

Answer:

Ellie drove 90 miles in three hours.

Step-by-step explanation:

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2 years ago

A bag of marbles contains 5 red, 3 blue, 2 green, and 2 yellow marbles. What is the probability that you choose a blue marble an

ira [324]

PART ANSWER:

Hi. I don't know the entire answer but I do know the probability of chosing a blue marble once is 25%.

5 + 3 + 2 + 2 = 12

3/12 or 1/4 = 25% or .25

Sorry I could not fully help.

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3 years ago

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