A teen chewing bubble gum blows a huge bubble, the volume of which satisfies the differential equation:dV/dt=2(V)^(0.5)Where t is the time in seconds after the teen start to blow the bubble. If the bubble pops as soon as it reaches 529 cubic centimeters in volume, how many seconds does it take for the bubble to pop? Assume that the bubble had no volume when the teen first started blowing.

The ODE is separable:

Integrate both sides to get

Assuming the bubble starts with zero volume, so that , we find

Then the volume of the bubble at time is

and so the time it take for the bubble to reach a volume of 629 cubic cm is

or 23 seconds after the teen first starts blowing the bubble.

x=17

step-by-step explanation:

solve 3x-24=x+10

then that makes it 2x=34 because you subtract an x from both sides to get rid of the one on the right, and then you add 24 to both sides to get rid of the 24 on the left

divide by both sides by 2 to get your answer so that you can get your answer