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3 years ago

For the graph y = 4 find the slope of a line that is perpendicular to it.

Mathematics

1 answer:

marusya05 [52]3 years ago

8 0

Answer:

Slope is 4

slope of the line perpendicular to it: x=-1/4

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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

A student raises her grade average from a 75 to a 90. What was the percent of increase in the student’s grade average? Round you

Zigmanuir [339]

=(new-old)/old *100%
=(90-75)/75 *100%
=20%
<span> hope it helps</span>

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3 years ago

¿Cuál es el ángulo complementario de 9°?<br>

Ann [662]

Answer:

90 - 9 = 81°

Step-by-step explanation:

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Cloud [144]

It depends how many decimal points you are moving. If it's 1 decimal point then the point would move to the right and the answer would be 3246.50if it was two decimal places then it moves two to the right and the answer would 32465.0. But you don't need to put the .0 at the end so it will be 32465

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Which graph represents y = RootIndex 3 StartRoot x minus 5 EndRoot?

Anika [276]

Answer:d

Step-by-step explanation:

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