Find the value of x to the nearest tenth.

Mathematics

1 answer:

Komok [63]3 years ago

6 0

Answer:

Step-by-step explanation:

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Substitution method<br> x=2y<br> 2x+5y=4

Dvinal [7]

Answer:

y=4/9

Step-by-step explanation:

Substitute 2y into the x

2(2y)+5y=4

4y+5y=4

9y=4

y=4/9

6 0

3 years ago

Suppose a tank contains 400 gallons of salt water. If pure water flows into the tank at the rate of 7 gallons per minute and the

Strike441 [17]

Answer:

Step-by-step explanation:

This is a differential equation problem most easily solved with an exponential decay equation of the form

$y=Ce^{kt}$ . We know that the initial amount of salt in the tank is 28 pounds, so

C = 28. Now we just need to find k.

The concentration of salt changes as the pure water flows in and the salt water flows out. So the change in concentration, where y is the concentration of salt in the tank, is $\frac{dy}{dt}$ . Thus, the change in the concentration of salt is found in

$\frac{dy}{dt}=$ inflow of salt - outflow of salt

Pure water, what is flowing into the tank, has no salt in it at all; and since we don't know how much salt is leaving (our unknown, basically), the outflow at 3 gal/min is 3 times the amount of salt leaving out of the 400 gallons of salt water at time t:

$3(\frac{y}{400})$