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Shalnov [3]
3 years ago
14

The line that passes through the point (2, −8) and has a slope of −1 is given by the equation y +

Mathematics
1 answer:
lilavasa [31]3 years ago
6 0

Answer:

y = -x+6

Step-by-step explanation:

We can use the slope intercept form

y = mx+b  where m is the slope and b is the y intercept

y = -1x+b

Substitute the point into the equation

-8 = -1*2 +b

-8 = -2+b

-8+2 = -2+b+2

-6 =b

y = -x+6

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Answer:

dQ(t)/dt = 20 - 2Q(t)/5 , Q(0) = 0

Step-by-step explanation:

The mass flow rate dQ(t)/dt = mass flowing in - mass flowing out

Since 5 g/L of salt is pumped in at a rate of 4 L/min, the mass flow in is thus 5 g/L × 4 L/min = 20 g/min.

Let Q(t) be the mass present at any time, t. The concentration at any time ,t is thus Q(t)/volume = Q(t)/10. Since water drains at a rate of 4 L/min, the mass flow out is thus, Q(t)/10 g/L × 4 L/min = 2Q(t)/5 g/min.

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dQ(t)/dt = 20 g/min - 2Q(t)/5 g/min

Since the salt just begins to be pumped in, the initial mass of salt in the tank is zero. So Q(0) = 0

So, the initial value problem is thus

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