Question

The rate (in liters per minute) at which water drains from a tank is recorded at half-minute intervals. Use the average of the left- and right-endpoint approximations to estimate the total amount of water drained during the first 3 min. t (min) 0 0.5 1 1.5 2 2.5 3 r (l/min) 44 40 37 34 30 27 23

Answer 1

Answer:

100.75 liters

Step-by-step explanation:

Data provided in the question:

t (min)     0     0.5      1     1.5      2      2.5      3

r (l/min)    44    40     37     34     30     27      23

Now,

left endpoint approximation

= 0.5 × ( 44 + 40 + 37 + 34 + 30 + 27 )

= 0.5 × 212

= 106

Right endpoint approximation

= 0.5 × ( 40 + 37 + 34 + 30 + 27 + 23 )

= 0.5 × 191

= 95.5

Therefore,

the average of the left- and right-endpoint approximations

= [ 106 + 95.5 ] ÷ 2

= 100.75 liters

Answer 2

The total amount of water drained during the first 3 min is: 100.75 liters/min.

Total amount of water

Left endpoint approximation

r = 1/2 ( 44 + 40 + 37 + 34 + 30 + 27 )

r= 1/2 × 212

r= 106 L/m

Right endpoint approximation

r= 1/2 × ( 40 + 37 + 34 + 30 + 27 + 23 )

r= 1/2 × 191

r= 95.5 L/min

Average of the left- and right-endpoint approximations

Average= [ 106 + 95.5 ] ÷ 2

Average=201.5÷2

Average= 100.75 liters/min

Inconclusion the total amount of water drained during the first 3 min is: 100.75 liters/min.

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