All categories

3 years ago

Please Help Me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Mathematics

2 answers:

yawa3891 [41]3 years ago

7 0

It doesn’t show anything?

AfilCa [17]3 years ago

3 0

Ok I will help you but..There’s a picture but it’s all grey.......

You might be interested in

If f(x, y, z) = x sin(yz), (a) find the gradient of f and (b) find the directional derivative of f at (2, 4, 0) in the direction

valentina_108 [34]

Answer:

a) $\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$ .

b) $Du_{f}(2,4,0) = -\frac{8}{\sqrt{11}}$

Step-by-step explanation:

Given a function $f(x,y,z)$ , this function has the following gradient:

$\nabla f(x,y,z) = f_{x}(x,y,z)\mathbf{i} + f_{y}(x,y,z)\mathbf{j} + f_{z}(x,y,z)\mathbf{k}$ .

(a) find the gradient of f

We have that $f(x,y,z) = x\sin{yz}$ . So

$f_{x}(x,y,z) = \sin{yz}$

$f_{y}(x,y,z) = xz\cos{yz}$

$f_{z}(x,y,z) = xy \cos{yz}$ .

$\nabla f(x,y,z) = f_{x}(x,y,z)\mathbf{i} + f_{y}(x,y,z)\mathbf{j} + f_{z}(x,y,z)\mathbf{k}$ .

$\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$

(b) find the directional derivative of f at (2, 4, 0) in the direction of v = i + 3j − k.

The directional derivate is the scalar product between the gradient at (2,4,0) and the unit vector of v.

We have that:

$\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$

$\nabla f(2,4,0) = \sin{0}\mathbf{i} + 0\cos{0}\mathbf{j} + 8 \cos{0}\mathbf{k}$ .

$\nabla f(2,4,0) = 0i+0j+8k=(0,0,8)$

The vector is $v = i + 3j - k = (1,3,-1)$

To use v as an unitary vector, we divide each component of v by the norm of v.

$|v| = \sqrt{1^{2} + 3^{2} + (-1)^{2}} = \sqrt{11}$

$v_{u} = (\frac{1}{\sqrt{11}}, \frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}})$

Now, we can calculate the scalar product that is the directional derivative.

$Du_{f}(2,4,0) = (0,0,8).(\frac{1}{\sqrt{11}}, \frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}}) = -\frac{8}{\sqrt{11}}$

6 0

3 years ago

-4(w+1)=-24<br><br> what does w equal?

makvit [3.9K]

Answer:

w=5

Step-by-step explanation:

using the distributive property to simplify the equation

-4(w)+1(-4)=-24 so

-4w-4=-24 (adding 4 to both sides)

-4w==20 (divide by -4)

w=5

8 0

3 years ago

Read 2 more answers

Mark just landed a great job as an engineer where he will make $65,000 a year. The company he will work for guarantees a 2% pay

dalvyx [7]

Answer:

65000(1.02)^n.

Step-by-step explanation:

Salary = 65000(1.02)^n where n is the number of years he has worked for the company.

So after one year he earns $6500* 1.02 and after 2 years $65000 * 1.02^2.

5 0

3 years ago

When an electronics company produces 1000 chips, it makes a profit of $10 per unit. When it produces 5000 chips, the company mak

adell [148]

I would be -198 your welcome :)

6 0

3 years ago

Simplify: √8x^5+ x√18x^3<br>÷x^2√50x

Sergeu [11.5K]

Answer:

10x^2 √2x

Step-by-step explanation:

hope this helps

lmk if it's wrong

7 0

3 years ago