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Airida [17]
4 years ago
15

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

Mathematics
1 answer:
Ipatiy [6.2K]4 years ago
6 0
Where’s the problem
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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, _ , _.<br> (Geometric and arithmetic sequences)
Alika [10]

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

<u>Step-by-step explanation:</u>

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]
<span>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.</span>
6 0
4 years ago
Read 2 more answers
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