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3 years ago

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can anyone help me is math please I can describe a real-world situation in which opposite quantities combine to make zero. I can

represent addition and subtraction on vertical and horizontal number line diagrams. I can demonstrate how to add two numbers using absolute value and a number line diagram. I can interpret sums of rational numbers by describing real-world situations.

1 answer:

asambeis [7]3 years ago

5 0

When you put money in the bank and then go to the store and write a check for that exact amount.

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Use the Chain Rule (Calculus 2)

atroni [7]

1. By the chain rule,

$\dfrac{\mathrm dz}{\mathrm dt}=\dfrac{\partial z}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial z}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}$

I'm going to switch up the notation to save space, so for example, $z_x$ is shorthand for $\frac{\partial z}{\partial x}$ .

$z_t=z_xx_t+z_yy_t$

We have

$x=e^{-t}\implies x_t=-e^{-t}$

$y=e^t\implies y_t=e^t$

$z=\tan(xy)\implies\begin{cases}z_x=y\sec^2(xy)=e^t\sec^2(1)\\z_y=x\sec^2(xy)=e^{-t}\sec^2(1)\end{cases}$

$\implies z_t=e^t\sec^2(1)(-e^{-t})+e^{-t}\sec^2(1)e^t=0$

Similarly,

$w_t=w_xx_t+w_yy_t+w_zz_t$

where

$x=\cosh^2t\implies x_t=2\cosh t\sinh t$

$y=\sinh^2t\implies y_t=2\cosh t\sinh t$

$z=t\implies z_t=1$

To capture all the partial derivatives of $w$ , compute its gradient:

$\nabla w=\langle w_x,w_y,w_z\rangle=\dfrac{\langle1,-1,1\rangle}{\sqrt{1-(x-y+z)^2}}}=\dfrac{\langle1,-1,1\rangle}{\sqrt{-2t-t^2}}$

$\implies w_t=\dfrac1{\sqrt{-2t-t^2}}$

2. The problem is asking for $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial y}$ . But $z$ is already a function of $x,y$ , so the chain rule isn't needed here. I suspect it's supposed to say "find $\frac{\partial z}{\partial s}$ and $\frac{\partial z}{\partial t}$ " instead.

If that's the case, then

$z_s=z_xx_s+z_yy_s$

$z_t=z_xx_t+z_yy_t$

as the hint suggests. We have

$z=\sin x\cos y\implies\begin{cases}z_x=\cos x\cos y=\cos(s+t)\cos(s^2t)\\z_y=-\sin x\sin y=-\sin(s+t)\sin(s^2t)\end{cases}$

$x=s+t\implies x_s=x_t=1$

$y=s^2t\implies\begin{cases}y_s=2st\\y_t=s^2\end{cases}$

Putting everything together, we get

$z_s=\cos(s+t)\cos(s^2t)-2st\sin(s+t)\sin(s^2t)$

$z_t=\cos(s+t)\cos(s^2t)-s^2\sin(s+t)\sin(s^2t)$

8 0

3 years ago

PLEASSEEEE HELP W THIS QUESTION!!!!

brilliants [131]

X/28 = 5/7
x = 28 * 5 / 7
x = 20

answer
x = 20 ft

3 0

3 years ago

Read 2 more answers

Find the product.<br> 5x2.2y2

ozzi

Answer:10x^2y^2

Step-by-step explanation:

5x2 X 2y2=10x^2y^2

3 0

3 years ago

Please help with my math work !<br> due tomorrow morning

Y_Kistochka [10]

Answer:

$y=2x+6$

Hope This Helps! :)

3 0

2 years ago

Whats -5n+12n+9+(-3) some one help me with this one

nikdorinn [45]

$-5n+12n+9+(-3)$

$-5n+12n+9-3$

$7n+9-3$

$=7n+6$

Hope this helps!

Thank you for posting your question at here on Brainly.

-Charlie

8 0

3 years ago