3. Solve for x. Round to the nearest tenth * 25 16 22 Your answer

Use the Chain Rule to find the indicated partial derivatives. u = x2 + yz, x = pr cos(θ), y = pr sin(θ), z = p + r; (partial u)/

devlian [24]

$u(x,y,z)=x^2+yz$

$\begin{cases}x(p,r,\theta)=pr\cos\theta\\y(p,r,\theta)=pr\sin\theta\\z(p,r,\theta)=p+r\end{cases}$

At the point $(p,r,\theta)=(2,2,0)$ , we have

$\begin{cases}x(2,2,0)=4\\y(2,2,0)=0\\z(2,2,0)=4\end{cases}$

Denote by $f_x:=\dfrac{\partial f}{\partial x}$ the partial derivative of a function $f$ with respect to the variable $x$ . We have

$\begin{cases}u_x=2x\\u_y=z\\u_z=y\end{cases}$

The Jacobian is

$\begin{bmatrix}x_p&x_r&x_\theta\\y_p&y_r&y_\theta\\z_p&z_r&z_\theta\end{bmatrix}=\begin{bmatrix}r\cos\theta&p\cos\theta&-pr\sin\theta\\r\sin\theta&p\sin\theta&pr\cos\theta\\1&1&0\end{bmatrix}$

By the chain rule,

$u_p=u_xx_p+u_yy_p+u_zz_p=2xr\cos\theta+zr\sin\theta+y$

$u_p(2,2,0)=2\cdot4\cdot2\cos0+4\cdot2\sin0+0\implies\boxed{u_p(2,2,0)=16}$

$u_r=u_xx_r+u_yy_r+u_zz_r=2xp\cos\theta+zp\sin\theta+y$

$u_r(2,2,0)=2\cdot4\cdot2\cos0+4\cdot2\sin0+0\implies\boxed{u_r(2,2,0)=16}$

$u_\theta=u_xx_\theta+u_yy_\theta+u_zz_\theta=-2xpr\sin\theta+zpr\cos\theta$

$u_\theta(2,2,0)=-2\cdot4\cdot2\cdot2\sin0+4\cdot2\cdot2\cos0\implies\boxed{u_\theta(2,2,0)=16}$

7 0

3 years ago

Plz help thank you :) Karen spent $32 on fruit at the grocery store. She spent a total of $40 at the store. What percentage of t

Lostsunrise [7]

32 is 80% of 40. Karen spent 80% on fruit and 20% on misc items.
Answer: 80%

7 0

3 years ago

Read 2 more answers

Fill in the gaps in this sequence: -8, -19, -30, _ , _. (Geometric and arithmetic sequences)

Alika [10]

-8, -19, -30, -49 , -60

Step-by-step explanation:

Here we have the following sequence :

-8, -19, -30, _ , _

First term of sequence is -8 .
Second term of sequence is -19 : $-8-11 = -19$
Third term of sequence is -30 : $-19-11 = -30$
Fourth term of sequence is : $-30-11 = -49$
Fifth term of sequence is : $-49-11 = -60$

Following sequence was an AP( Arithmetic Progression ) with first term as -8 i.e. $a = -8$ and common difference $d = -11$ having general equation as : $-8 -11n$ .

6 0

4 years ago

How many solutions does this system have?

Sunny_sXe [5.5K]

Answer:

there is one solution in my opinion

Step-by-step explanation:

3 0

4 years ago

What does a persuasive visual designed to make an argument refer to a. visual rhetoric b. logos c. pathos

Mkey [24]

a) Visual Rhetoric. Logos means creating a symbol for some fixed thing. Pathos is related to evoking pity or sadness. Both these are clearly can't be the answer. Visual Rhetoric means using visual images to communicate meaning. This includes using visual design to make an argument. So this should be the answer.

6 0

4 years ago

Read 2 more answers