Water flows into a tank according to the rate f(t) = (6+t)/(1+t), and at the same time empties out at the rate e(t) = ln (t+2)/(t+1), with both f(t) and e(t) measured in gallons per minute. how much water, to the nearest gallon, is in the tank at time t = 10 minutes.

F(t) = 1.5 gallon /min

E(t) = 5.5 gallon/min

Step-by-step explanation:

The rate at which water flows into the tank = F(t)

The rate at which water is emptied from the tank = E(t)

F(t) = (6+t)/(1+t)

E(t) = ln (t+2)/(t+1)

When t = 10 mins

F(t) = (6 + 10)/(1+10)

= 16/11

F(t) = 1.5 gallon /min

E(t) = ln (10 +2)(10+1)

= ln(12)(20)

= ln(240)

E(t) = 5.5 gallon/min

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.