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3 years ago

Which of the following expressions is equivalent to

2 answers:

7 0

First what I do is take separate x's and y's inside the ( ) then I like to put the x's and y's off to the side so then if you take 6+12 you get 18 but you have to multiply by 1/2 or divide by two and you get 9 that means that the answer is A because one of the y's is + the other is -

ivanzaharov [21]3 years ago

3 0

$\frac{1}{2}y^2 (6x + 2y+12x-2y)\\\\= \frac{1}{2}y^2 (18x)\\\\=9xy^2$

A) 9xy²

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Suppose a different student reaches in the bag, randomly selects their twenty chips, and estimates that 60% of the students are

djyliett [7]

12 chips if you are trying to find 60% of 20

8 0

4 years ago

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

What is the arc measure of DBC in degree

aliya0001 [1]

The length of both AB and DC is the same.

19 degrees

We want to know the arc measure for the whole circle, except for DC. So, we can subtract the arc measure of DC from 360 to find DBC. Since we found DC above, all we need to do is subtract.

360 - 19 = 341

DBC = 341 degrees

Hope this helps!! :)

8 0

3 years ago

Which is f(6) for the quadratic function graphed? 0 -2 * -0.5 1.5 4

rusak2 [61]

Answer:

Step-by-step explanation:

I'm pretty sure theres a graph to this so....

The given parabolic graph of quadratic function

To find:What is F(6) for the quadratic function

Solution:We have given graph of quadratic function

there is a different value for Y and a different value for X

For f(6)

here X=6, need to find graph of quadratic function

X=6

f(6)=4

Y=4

Your welcome :)

4 0

3 years ago

J'aime rendre la vie des gens difficile si vous n'aimez pas cette question

Alona [7]

Answer:

No te gustará cuando la gente te haga la vida tan difícil (:

Jus remeber karama todavía está viva

7 0

3 years ago

Read 2 more answers