Answer:
dy/dt = 7y / (t − 1000)
Step-by-step explanation:
Change in mass of salt = mass of salt going in − mass of salt going out
dy/dt = 0 − (C kg/L × 7 L/min)
where C is the concentration of salt in the tank.
The concentration is mass divided by volume:
C = y / V
The volume in the tank as a function of time is:
V = 1000 + 6t − 7t
V = 1000 − t
Therefore:
C = y / (1000 − t)
Substituting:
dy/dt = -7y / (1000 − t)
dy/dt = 7y / (t − 1000)
If we wanted, we could separate the variables and integrate. But the problem only asks that we find the differential equation, so here's the answer.
Answer:
2/7
Step-by-step explanation:
by dividing both numerator and denominator by 5
The slope intercept of 6x - 2y = 10 is 3.
Use the slope intercept form y = mx + b to find the slope m and y-intercept b.
Answer:
√2
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A counterexample for the expression secФ / tanФ = sinФ is 45°
This is a FALSE statement.
Explanation:
Solving Right-hand side:
SecФ = 1 / CosФ
tanФ = SinФ / CosФ
secФ/tanФ = 1 / CosФ ÷ SinФ / CosФ
secФ/tanФ = 1 / CosФ × CosФ/SinФ
secФ/tanФ = CosФ / SinФCosФ
secФ/tanФ = 1 / SinФ
Hence,
Left-hand side ≠ Right-hand side
