40% of N is 80. Find N

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

2 years ago

Anyone know ??? i need help badly right now

Brilliant_brown [7]

Answer:

Answer is A 520mm²

I hope you like it

3 0

2 years ago

Read 2 more answers

Find the volume of this square based pyramid. 5 cm 5 cm 5 cm. Round to the nearest tenth.

vodka [1.7K]

Answer:

41.666 cm³ or 41.7 cm³ rounded to the nearest tenth.

Step-by-step explanation:

Volume of a square pyramid = base length² × height ÷ 3

25 × 5/3 = 41. 666

Have a great day:)

4 0

2 years ago

An isosceles triangle has an angle that measures 92° which other angles could be in that isosceles triangle choose all that appl

nignag [31]

Answer:

44

Step-by-step explanation:

The two base angles cannot both be 92 degrees because they would add up to 184 which is more degrees than any triangle has. The apex angle (the top angle) therefore has 92 degrees.

The base angles are equal and found as follows.

2*b + 92 = 180 Subtract 92 from both sides

2b +92-92 = 180-92

2b = 88 divide by 2

2b/2=88/2

b = 44

The only angle measurement that fits is 44

6 0

2 years ago

It takes Santa 5 minutes to fly 35 miles with the wind .It takes him 7 minutes to fly 35 miles against the wind determine the sp

Dmitrij [34]

Answer: Santa's speed in still air is 6 miles per minute

Speed of the wind is 1 mile per minute

Step-by-step explanation:

Let x represent the speed of Santa in still air. It is assumed that in still air. She is flying with the wind. If the speed of the wind is y, then him total speed is x + y

It takes Santa 5 minutes to fly 35 miles with the wind.

Speed = distance / time

It means that

x + y = 35/5 = 7

It takes him 7 minutes to fly 35 miles against the wind. This means that his total speed will be x - y

Speed = distance/time. Therefore,

x - y = 35 /5 = 5 - - - - - - 1

Substituting x = 7 - y into equation 1, it becomes

7 - y - y = 5

-2y = 5 - 7 = -2

y = -2/-2 = 1

x = 7 - y = 7 - 1

x = 6

3 0

2 years ago