A water park has pools, slides, and rides that, in total, make use of 8, point, 6, times, 10, to the power 58.6×10^5 gallons of water. They plan to add a ride that would make use of an additional 9, point, 1, times, 10, to the power 49.1×10^4 gallons of water. Use scientific notation to express the total gallons of water made use of in the park after the new ride is installed.
To calculate the total gallons of water after the new ride is installed, we need to add the amount of water from the existing pools, slides, and rides to the amount of water needed for the new ride.
Existing water usage: 8.6 x 10^58.6 gallons
New ride water usage: 9.1 x 10^49.1 gallons
Total water usage = (8.6 x 10^58.6) + (9.1 x 10^49.1)
To add these numbers, we need to make sure the exponents are the same. Let's convert 8.6 x 10^58.6 into scientific notation with a power of 49.1:
8.6 x 10^58.6 = 0.86 x 10^59.6
Now, we can add:
Total water usage = (0.86 x 10^59.6) + (9.1 x 10^49.1)
Total water usage = 0.86 x 10^59.6 + 0.91 x 10^49.1
Total water usage = 0.86 x 10^59.6 + 0.000091 x 10^59.6
Total water usage = 0.860091 x 10^59.6 gallons
Therefore, in scientific notation, the total gallons of water made use of in the park after the new ride is installed is 8.6 x 10^59.6 gallons.