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3 years ago

-1/2, -2, -8, -32 Is this geometric, arithmetic, or neither?

Mathematics

1 answer:

serg [7]3 years ago

4 0

Answer:

Neither

Step-by-step explanation:

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Find the directional derivative of f(x,y,z)=z3−x2yf(x,y,z)=z3−x2y at the point (−5,5,2)(−5,5,2) in the direction of the vector v

olga_2 [115]

We are given

$f=z^3 -x^2y$

Firstly, we can find gradient

so, we will find partial derivatives

$f_x=0 -2xy$

$f_x=-2xy$

$f_y=0 -x^2$

$f_y=-x^2$

$f_z=3z^2$

now, we can plug point (-5,5,2)

$f_x=-2*-5*5=50$

$f_y=-(-5)^2=-25$

$f_z=3(2)^2=12$

so, gradient will be

$gradf=(50,-25,12)$

now, we are given that

it is in direction of v=⟨−3,2,−4⟩

so, we will find it's unit vector

$|v|=\sqrt{(-3)^2+(2)^2+(-4)^2}$

$|v|=\sqrt{29}$

now, we can find unit vector

$v'=(\frac{-3}{\sqrt{29} } , \frac{2}{\sqrt{29} } , \frac{-4}{\sqrt{29} })$

now, we can find dot product to find direction of the vector

$dir=(gradf) \cdot (v')$

now, we can plug values

$dir=(50,-25,12) \cdot (\frac{-3}{\sqrt{29} } , \frac{2}{\sqrt{29} } , \frac{-4}{\sqrt{29} })$

$dir=(-\frac{150}{\sqrt{29} } - \frac{50}{\sqrt{29} } - \frac{48}{\sqrt{29} })$

$dir=-\frac{248\sqrt{29}}{29}$ .............Answer

7 0

3 years ago

Read 2 more answers

Help..... me .......please..........ITS URGENT

Vikentia [17]

Answer: 115, 2645

(x= 115, y= 2645)

Step-by-step explanation:

There are two methods to this, which is using the graph with each x and y value, or substituting in values.

I would suggest looking at the graph first and then substituting values so you know the equation is being satisfied by the ordered pair.

In this case, one way to check it could look like this (substituting y value):

y = 23x

2645 = 23x

x = 2645÷23

x = 115

6 0

2 years ago

What is 25% as a decimal

Artist 52 [7]

25% as a fraction is 1/4 or 25/100 so as a decimal its 1/4 of 1 which is .25

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3 years ago

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QUESTION IN PICTURE thx <3

Umnica [9.8K]

Answer:

7 1/9

Step-by-step explanation:

because I know i'm right

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3 years ago

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I need help on this question

barxatty [35]

I believe this is pythag

15^2 x 11^2 = 27225

(square root) of 27225 = 165

165ft

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3 years ago