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Brilliant_brown [7]
3 years ago
10

Example 2.3.6. Consider a fish tank that initially contains 150 liters of water with 20 grams of salt (pollutant) dissolved in i

t. The salt concentration in the tank needs to be increased from 20/150 grams per liter to 1 gram per liter to accommodate a new species of fish. Water containing 3 grams of salt per liter is allowed to run into the tank at a rate of 2 liters per minute. The thoroughly stirred mixture in the tank is also allowed to drain out at the same rate of 2 liters per minute. Find a differential equation for the amount of salt x(t) in the tank at time t. Use the initial condition x(0) = 20 to find the time it will take to increase the salt concentration in the tank to 1 gram per liter.
Mathematics
1 answer:
Serjik [45]3 years ago
4 0

Answer:

sorry I clicked on the question and couldn't get out of it

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John paid $222 for four hours of skiing and two hours boating. He paid $213 for two hours skiing and three hours boating. What i
Inga [223]

Answer:

Skiing costs $30 per hour and Boating costs $51 per hour.

Step-by-step explanation:

Let cost per hour of skiing be x and cost per hour of boating be y. Let's dissect the problem into 2 simultaneous equations.

<em><u>"John paid $222 for four hours of skiing and two hours boating":</u></em>

4x+2y=222

<em><u>"He paid $213 for two hours skiing and three hours boating":</u></em>

2x+3y=213

<em>Now, if we solve for x in the 2nd equation and plug it in the 1st equation, we will have the value for y</em>. Work shown below.

2x+3y=213\\2x=213-3y\\x=\frac{213-3y}{2}\\Equation 1: 4x+2y=222\\Substituting :\\4(\frac{213-3y}{2})+2y=222\\2(213-3y)+2y=222\\426-6y+2y=222\\426-222=6y-2y\\204=4y\\y=\frac{204}{4}=51

Hence, y = 51

<em>Now, substituting this y value into the 1st equation and solving for x will give us the value of x.</em>

First Equation: 4x+2y=222\\4x+2(51)=222\\4x+102=222\\4x=222-102\\4x=120\\x=\frac{120}{4}=30

Hence, skiing costs $30 per hour and boating costs $51 per hour.

4 0
3 years ago
Write the slope intercept form of the equation of each line <br> X-4y=-12
natka813 [3]

Answer:

y=-1/4x+3

Step-by-step explanation:

5 0
4 years ago
A pair of pants originally cost $15 and are 10% off. In addition, you have a coupon to get another 20% off. How much will the pa
Archy [21]
$10.50 and 6/9

hope this helps!
7 0
4 years ago
Which goes to this inequality x + 1 &lt; 3
Serggg [28]
I got x < 2 for the inequality
Look at the image for more information

7 0
3 years ago
Hiii! can someone please help me with my maths question
beks73 [17]

Step-by-step explanation:

a^2 + b^2 = c^2

(x+2)^2 + 4x^2 = (3x+4)^2

(x+2)(x+2)+ 4x^2= (3x+4)(3x+4)

x^2 + 2x + 2x + 4 + 4x^2 = 9x^2 + 12x + 12 x + 16

5x^2 + 4x + 4 = 9x^2 + 24x + 16

-4x^2 - 20x - 12 = 0

now we can use the quadratic formula

(-b±√(b²-4ac))/(2a)

I can't type all this so

.....

x = -0.697224362 or -4.302775638

AB can't be negative so it's the first one

so it's equals to 1.302775638

6 0
3 years ago
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