Question

The volume of one cloud, in cubic kilometers, grows according to the expression 43x – 1, where x is time in hours. Another cloud grows according to the expression 8x. After how many hours will the two clouds have the same volume? What is their volume, in cubic kilometers?

Answer 1

After approximately 0.0286 hours, the two clouds will have the same volume, which is 8/35 cubic kilometers.

Step-by-step explanation:

We are given the volume functions of two clouds: 43x - 1 and 8x, where x represents time in hours. We need to find the time at which the volume of both clouds is the same and the value of this volume.

To find the time at which the volume of both clouds is the same, we set the two expressions equal to each other:

43x - 1 = 8x

Now, we can solve this equation to find the value of x. Adding 1 to both sides, we get:

43x - 1 + 1 = 8x + 1

43x = 8x + 1

Subtracting 8x from both sides, we get:

43x - 8x = 8x + 1 - 8x

35x = 1

Dividing both sides by 35, we find:

x = 1/35

So after 1/35 hours, or approximately 0.0286 hours, the two clouds will have the same volume.

To find the volume at this time, we substitute the value of x back into either of the volume expressions. Let's use the expression 43x - 1:

Volume = 43(1/35) - 1

Volume = 43/35 - 1

Volume = (43 - 35)/35

Volume = 8/35

So at the time when the two clouds have the same volume, their volume is 8/35 cubic kilometers.