Emma baker 14 cookies she sold 2/7 of the cookies how many cookies did Emma sell?

Use the Chain Rule to find the indicated partial derivatives. z = x^4 + xy^3, x = uv^4 + w^3, y = u + ve^w Find : ∂z/∂u , ∂z/∂v

k0ka [10]

I'll use subscript notation for brevity, i.e. $\frac{\partial f}{\partial x}=f_x$ .

By the chain rule,

$z_u=z_xx_u+z_yy_u$

$z_v=z_xx_v+z_yy_v$

$z_w=z_xx_w+z_yy_w$

We have

$z=x^4+xy^3\implies\begin{cases}z_x=4x^3+y^3\\z_y=3xy^2\end{cases}$

and

$\begin{cases}x=uv^4+w^3\\y=u+ve^w\end{cases}\implies\begin{cases}x_u=v^4\\x_v=4uv^3\\x_w=3w^2\\y_u=1\\y_v=e^w\\y_w=ve^w\end{cases}$

When $u=1,v=1,w=0$ , we have

$\begin{cases}x(1,1,0)=1\\y(1,1,0)=2\end{cases}\implies\begin{cases}z_x(1,2)=12\\z_y(1,2)=12\end{cases}$

and the partial derivatives take on values of

$\begin{cases}x_u(1,1,0)=1\\x_v(1,1,0)=4\\x_w(1,1,0)=0\\y_u(1,1,0)=1\\y_v(1,1,0)=1\\y_w(1,1,0)=1\end{cases}$

So we end up with

$\boxed{\begin{cases}z_u(1,1,0)=24\\z_v(1,1,0)=60\\z_w(1,1,0)=12\end{cases}}$

3 0

3 years ago

Arrange the numbers in increasing order 14.204 14.200 14.240 14.210

Crank

Answer:

Arranging the numbers in increasing order is 14.200, 14.204, 14.210, 14.240.

Step-by-step explanation:

Given : Numbers 14.204, 14.200, 14.240, 14.210.

To find : Arrange the numbers in increasing order ?

Solution :

Arrange the numbers in increasing order is defined as arranging numbers from the smallest number to the largest number.

If we see the numbers 14.204, 14.200, 14.240, 14.210.

The number before decimal is same so we arrange according to after decimal,

14.200<14.204<14.210<14.240

Therefore, Arranging the numbers in increasing order is 14.200, 14.204, 14.210, 14.240.

5 0

3 years ago

It takes Ms. Campbell 5 times as long as it takes Ms. Dorsey to paint a room. If Ms. Dorsey

Aliun [14]

Answer:

Dorsey = 4.8 hours

Campbell = 24 hours

Step-by-step explanation:

It takes "x" hours for Dorsey

So, it will take 5 times more for Campbell, so

It takes "5x" hours for Campbell

Rate is inverse of time, so rates are:

Dorsey: 1/x

Campbell: 1/5x

We know Rate * Time = Work

When together, it takes 4 hours to finish a work, so we can write:

$(\frac{1}{x}+\frac{1}{5x})4=1$

Solving for x, we get the time of Dorsey:

$(\frac{1}{x}+\frac{1}{5x})4=1\\(\frac{1}{x}+\frac{1}{5x})=\frac{1}{4}\\\frac{5+1}{5x}=\frac{1}{4}\\\frac{6}{5x}=\frac{1}{4}\\5x=24\\x=4.8$

Dorsey takes 4.8 hours alone

Campbell takes 4.8 * 5 = 24 hours alone

7 0

3 years ago

Please help with this problem -9z = 2 - 10z

fgiga [73]

Answer:

z=2

Step-by-step explanation:

3 0

3 years ago

Kyle gave 2/7 of his money to his wife and spent 3/5 of the remainder. If he had $300 left, how much money did he have at first?

weqwewe [10]

Answer:

Kyle gave 2/7th of his money to his wife and spent 3/5 of the remainder. If he had $300 left, the money had by Kyle at first is $1050

Solution:

Step 1:

Consider “x” as the money which Kyle had initially.

From question, Kyle gave 2/7th of his money to his wife. So the remaining money left with Kyle is given as,

$= 1 - \frac{2}{7}$

$= \frac{7 - 2}{7} = \frac{5}{7}$ ----- eqn 1

Now the remaining money left with Kyle is 5/7th.Given that Kyle spent 3/5 of the remaining money.

Now the remaining money left with Kyle is given as

$= 1 - \frac{3}{5} = \frac{5 - 3}{5} = \frac{2}{5}$

Now kyle is left with $300, which is 2/5th of the initial money x .

We get equation as

$\frac{2}{5} x=300$

2x = 1500

x = 750

Now Kyle is left with 750$ which is 5/7th of the initial amount x.( by using eqn 1)

We get equation as

$\frac{5}{7} x = 750$

5x = 5250

x = 1050

So the amount had by Kyle at first is $1050

7 0

3 years ago