Answer:
The quantity of water in the tank after 15 days is 1610.0 gallons OR 1.61 × 10³ gallons.
Step-by-step explanation:
The amount of water in the tank after 15 days is given by the series
910+(−710)+810+(−610)+⋯+310+(−110)+210
From the series, we can observe that, if water is added for a particular day then water will be drained the following day.
Also, for a day when water is to be added, the quantity to be added will be 100 gallon lesser than the quantity that was last added. Likewise, for a day when water is to be drained, the quantity to be drained will be 100 gallons lesser than the quantity that was last drained.
Hence, we can complete the series thus:
910+(−710)+810+(−610)+710(-510)+610(-410)+510(-310)+410(-210)+310+(−110)+210
To evaluate this, we get
910-710+810-610+710-510+610-410+510-310+410-210+310-110+210
= 1610.0 gallons
Hence, the quantity of water in the tank after 15 days is 1610 gallons OR 1.61 × 10³ gallons.
The absolute value of -8 is 8 and the absolute value of 5 is 5. Absolute value is basically the number's distance from 0 on a number line, basically how many numbers it is away from 0. For that reason, it's always positive, regardless of whether or not the number is positive or negative. Hope this helped!
