Respuesta :
Answer:
The volume after 1 minute is 5314680 liters.
Step-by-step explanation:
We are given the following in the question:
[tex]\dfrac{dV}{dt}=r(t) = 18(1 + 2t)^2[/tex]
where r(t) is the rate in liters per second starting with a volume of 0 liters at time t = 0.
We have to find the volume of balloon after 1 minute.
We evaluate it in the following manner:
t = 60 and t = 0
[tex]V =\displaystyle\int^{60}_0 18(1 + 2t)^2~dt\\\\V = 18 \bigg [ \dfrac{(1+2t)^3}{(3)(2)}\bigg ]^{60}_0\\\\V = 3[(1+2(60))^3-(1+2(0))^3]\\V = 3(1771560)\\V = 5314680[/tex]
Thus, the volume after 1 minute is 5314680 liters.
The volume of the balloon after 1 minute is [tex]2.64*10^{5}[/tex] liters.
Given that, A balloon is being filled at a rate of,
[tex]r(t) = 18(1 + 2t) ^{2} lit/s[/tex]
We know that, 1 minute = 60 seconds
To find the volume of the balloon after 1 minute , substitute t = 60 in above expression.
[tex]r(60)=18(1+120)^{2}=2.64*10^{5} liters[/tex]
Hence, the volume of the balloon after 1 minute is [tex]2.64*10^{5}[/tex] liters.
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