Name the intersection of AE and CG

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

R = {10, 15, 20}

Umnica [9.8K]

Answer:

R n S = {20}

Step-by-step explanation:

n in sets means same elements found in the sets which are being compared

5 0

3 years ago

You look at real estate ads for houses in Naples, Florida. There are many houses ranging from $200,000 to $500,00 in price. The

cricket20 [7]

Answer:

c) skewed to the right.

Step-by-step explanation:

We need to remember that is a distribution is skewed to the right then we have the following condition satisfied:

$Mode< Median$

And if is skewed to the left then we have:

$Mean$

If the distribution is symmetric we need to satisfy:

$Mean = Median=Mode$

For this case since we have most of the values between 200000 and 500000 when we put atypical values like 15000000 that would affect the sample mean and on this case the sample mean would larger than the sample median because the median is a robust measure of central tendency not affected by outliers.

So for this special case we can say that the $Mean>Median$ . And probably the median would be higher than the mode so then we can conclude that the best answer for this case would be:

c) skewed to the right.

5 0

3 years ago

Determine if the following system of equations has no solutions, infinitely many

DochEvi [55]

Answer:

There is one solution

Step-by-step explanation:

2x + y = -1

8x + 3y = -2

Multiply the first equation by -4

-8x -4y = 4

Then add the equations together to eliminate x

-8x -4y = 4

8x + 3y = -2

--------------------

-y = 2

Multiply by -1

y =-2

Now find x

2x+y =-1

2x+-2 =-1

Add 2 to each side

2x-2+2=-1+2

2x=1

Divide by 2

x = 1/2

8 0

3 years ago

Which is the graph of the equation y-1=2/3(x-3)

Alexxandr [17]

The attachment is the graph of the equation y - 1 = 2 / 3 (x - 3)

4 0

4 years ago