an ice cream factory makes 310 quarts of ice cream in 5 hours. how many quarts could be made in 48 hrs? what is the rate.

2 answers:

4 0

The first step is seeing how many times 5 can go in 48. 5 can go in 48 9 times. Then you multiply 310 by 9 which equals 2790. Then you divide 310 by 5 which equals 62. Then you add 62 , three times, to 2790.
The final answer is 2979 quarts.

RSB [31]3 years ago

4 0

Hello , okay sooooo ...

You first divide the total quarts of ice cream made by the total hours it was made in

310 ÷ 5

The answer you get tells you how much ice cream can be made in 1 hour

310 ÷ 5 = 62

It is now proven that 62 quarts of ice cream can be made in 1 hour

To find out how much ice cream can be made in 48 hours you multiple 62 and 48

The product will give you the answer to this problem

2976 quarts of ice cream can be made in 48 hours

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zheka24 [161]

Answer:

1 cup of sugar per 2.5 cups of flour.

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Step-by-step explanation:

5 0

3 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.