What is 57,020,000 expressed in scientific notation

A lot of work but you're lucky cuz I am bored.

Because we were not given any specific point to start off with. I choose (2,2), which is shown in red as 1. Note that 1 box = 1 unit.

We translate it 2 times.
a) (x+5)(y+3) = (2+5)(2+3) = (7,5) is our new point (shown in brown as 2)
Translation process shown in yellow.

b) (x-4)(y+2) = (7-4)(5+2) = (3,7) is our final point (shown in orange as 3)
Note that we use the 2nd point for the second translation as required.
Translation process shown in lime.

We can therefore determine from the picture below that you can use the translation (x+1)(y+5), which the translation process is shown in blue.
Proof: (x+1)(y+5) = (2+1)(2+5) = (3,7)

Now let's do it again, except we do the second translation first and the first translation last.

c) (x-4)(y+2) = (2-4)(2+2) = (-2,4) is our new point (shown in purple as 4)
Translation process shown in pink.

d) (x+5)(y+3) = (-2+5)(4+3) = (3,7) is our final point (shown in orange as 3)
Translation process shown in dark blue.
Same rules as (b). Notice how the final point is still the same? Therefore it makes no difference.

Hope I helped a lot :P

4 0

3 years ago

A tank is filled with 1000 liters of pure water. Brine containing 0.04 kg of salt per liter enters the tank at 9 liters per minu

klemol [59]

Answer:

The differential equation which describes the mixing process is $\frac{dc_{salt,out}}{dt} + \frac{2}{125}\cdot c_{salt,out} = \frac{71}{100000}$ .

Step-by-step explanation:

The mixing process within the tank is modelled after the Principle of Mass Conservation, which states that:

$\dot m_{salt,in} - \dot m_{salt,out} = \frac{dm_{tank}}{dt}$

Physically speaking, mass flow of salt is equal to the product of volume flow of water and salt concentration. Then:

$\dot V_{water, in, 1}\cdot c_{salt, in,1} + \dot V_{water, in, 2} \cdot c_{salt,in, 2} - \dot V_{water, out}\cdot c_{salt, out} = V_{tank}\cdot \frac{dc_{salt,out}}{dt}$

Given that $\dot V_{water, in, 1} = 9\,\frac{L}{min}$ , $\dot V_{water, in, 2} = 7\,\frac{L}{min}$ , $c_{salt,in,1} = 0.04\,\frac{kg}{L}$ , $c_{salt, in, 2} = 0.05\,\frac{kg}{L}$ , $\dot V_{water, out} = 16\,\frac{L}{min}$ and $V_{tank} = 1000\,L$ , the differential equation that describes the system is:

$0.71 - 16\cdot c_{salt,out} = 1000\cdot \frac{dc_{salt,out}}{dt}$

$1000\cdot \frac{dc_{salt, out}}{dt} + 16\cdot c_{salt, out} = 0.71$

$\frac{dc_{salt,out}}{dt} + \frac{2}{125}\cdot c_{salt,out} = \frac{71}{100000}$

3 0

3 years ago