What is the area of a regular hexagon with a radius of 14 inches

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

PLZZZZZZZZ HELP ME I WILL GIVE BRAINLIEST TO THE FASTEST AND MOST ACCURATE

Triss [41]

Answer:

10/1 +54/-6

Step-by-step explanation:

Is this the answer?

4 0

3 years ago

Read 2 more answers

The car at each vertex of a Ferris wheel holds a maximum of 5 people. The sum of the measures of the angles of the Ferris wheel

larisa [96]

Answer:

225

Step-by-step explanation:

The sum total of all the angles is 7,740 degrees,

The formula for the interior angle is 180(n - 2) where n is the number of sides in the polygon

Set this equal to 7740

180 (n-2) = 7740

Divide each side by 180

180/180 (n-2) = 7740/180

n-2 =43

Add 2 to each side

n-2+2 = 43+2

n = 45

Each vertex hold 5 people so take n and multiply by 5

45*5 = 225

The Ferris wheel holds 225 people

3 0

3 years ago

I'm I right?????? because i think i am

Ilya [14]

$\sqrt{3x+10}=\sqrt{2x+3}\\\\\\\dfrac{\sqrt{3x+10}}{\sqrt{2x+3}}=1\\\\\\\sqrt{\dfrac{3x+10}{2x+3}}=1\\\\\\\dfrac{3x+10}{2x+3}=1\\\\\\3x+10 =2x+3\\\\x = -7$

7 0

3 years ago

Read 2 more answers

The base of a right pyramid is a regular hexagon with sides of length 12 m. The altitude is 6 m. Find the total surface area of

Eva8 [605]

Answer:

806.12 m

Step-by-step explanation:

Step 1: Write the data

Side (s) = 12

Altitude (h) = 6

Step 2: Write the formula for surface area of right hexagonal pyramid

Area = 3√3/2*s² + 3*s*√(h²+3s²/4)

Step 3: Substitute values of 's' and 'h'

Area = 3√3/2*(12)² + 3*(12)*√[6²+3(12)²/4]

Area = 806.12 m

Therefore, the total surface area of the pyramid is 806.12 m.

!!

4 0

3 years ago