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3 years ago

What is 1/4 • 16 equal

1 answer:

8 0

Hello!

Multiple: 1/4 x 16 = 1 x 16/4 x 1 = 164 = 4

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD( 16, 4)

The Correct Answer is "4"

Hope this Helps! :)

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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

2 years ago

8 times the difference between a number and 6 is equal to 4 times the number.

iVinArrow [24]

8(x - 6) = 4x
Distribute.
8x - 48 = 4x
Subtract 8x from both sides.
8x -8x - 48 =4x -8x
Now you have...
-48 = -4x
Divide -4 by both sides.
-48/-4 = -4x/-4
12 = x
The number is 12.

8 0

2 years ago

Read 2 more answers

I need to subtract it with renaming it too.

Vladimir79 [104]

$8 \frac{1}{6} -3 \frac{5}{6} = 7 \frac{7}{6} -3 \frac{5}{6}$
$= 4 \frac{2}{6} = 4 \frac{1}{3}$

6 0

3 years ago

Read 2 more answers

Help ASAP please hmmmm

Fiesta28 [93]

Answer:

20d + 30d

Step-by-step explanation:

20 and 30 minutes per day

5 0

2 years ago

Read 2 more answers

Kelly shows all the ways to make 49 as tens and ones. What ways does she show?

xeze [42]

Kelly can show 49 with 4 ten blocks and 9 one blocks, 49 ones blocks, and she take a one hundred grid block, places 4 tens on 4 columns of the 100 and 9 one blocks on one row of the 100 grid block.

7 0

3 years ago