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3 years ago

Find the distance between the two points in simplest radical form (−6, 1) and (−8,−4)

Mathematics

1 answer:

Elena L [17]3 years ago

7 0

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Initially a tank contains 10 liters of pure water. Brine of unknown (but constant) concentration of salt is flowing in at 1 lite

zhenek [66]

Answer:

Therefore the concentration of salt in the incoming brine is 1.73 g/L.

Step-by-step explanation:

Here the amount of incoming and outgoing of water are equal. Then the amount of water in the tank remain same = 10 liters.

Let the concentration of salt be a gram/L

Let the amount salt in the tank at any time t be Q(t).

$\frac{dQ}{dt} =\textrm {incoming rate - outgoing rate}$

Incoming rate = (a g/L)×(1 L/min)

=a g/min

The concentration of salt in the tank at any time t is = $\frac{Q(t)}{10}$ g/L

Outgoing rate = $(\frac{Q(t)}{10} g/L)(1 L/ min)$ $\frac{Q(t)}{10} g/min$

$\frac{dQ}{dt} = a- \frac{Q(t)}{10}$

$\Rightarrow \frac{dQ}{10a-Q(t)} =\frac{1}{10} dt$

Integrating both sides

$\Rightarrow \int \frac{dQ}{10a-Q(t)} =\int\frac{1}{10} dt$

$\Rightarrow -log|10a-Q(t)|=\frac{1}{10} t +c$ [ where c arbitrary constant]

Initial condition when t= 20 , Q(t)= 15 gram

$\Rightarrow -log|10a-15|=\frac{1}{10}\times 20 +c$

$\Rightarrow -log|10a-15|-2=c$

Therefore ,

$-log|10a-Q(t)|=\frac{1}{10} t -log|10a-15|-2$ .......(1)

In the starting time t=0 and Q(t)=0

Putting t=0 and Q(t)=0 in equation (1) we get

$- log|10a|= -log|10a-15| -2$

$\Rightarrow- log|10a|+log|10a-15|= -2$

$\Rightarrow log|\frac{10a-15}{10a}|= -2$

$\Rightarrow |\frac{10a-15}{10a}|=e ^{-2}$

$\Rightarrow 1-\frac{15}{10a} =e^{-2}$

$\Rightarrow \frac{15}{10a} =1-e^{-2}$

$\Rightarrow \frac{3}{2a} =1-e^{-2}$

$\Rightarrow2a= \frac{3}{1-e^{-2}}$

$\Rightarrow a = 1.73$

Therefore the concentration of salt in the incoming brine is 1.73 g/L

8 0

3 years ago

What is the reason for an outlier in a graph?

Anna71 [15]

It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500) while others may indicate that something unusual is happening

7 0

3 years ago

Can someone please help

Leona [35]

Answer:

each hamburger costs $3.50

Step-by-step explanation:

he spent $13 in total and bought one hot dog for $2.50 and 3 hamburgers but we don't know the price of one hamburger so we could represent it by the equaton,

2.50 + 3h = 13 now solve for x

-2.50 2.50

3h = 10.50

h=3.50

check:

2.50+3(3.50)=13

2.50+10.50=13

13=13

4 0

3 years ago

HELP PLZZZZZ ASAP

Deffense [45]

Answer: $22.50

Step-by-step explanation:

25% of 30 = 7.5

30 - 7.5 = 22.50

5 0

3 years ago

Read 2 more answers

Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(−2, 1), B(3, 1), C(3, 4),

Lynna [10]

Answer:

16 units.

Step-by-step explanation:

8 0

2 years ago