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The rate at which sand is poured into a bag is modeled by the function r given by r(t)=15t−2t2, where r(t) is measured in milliliters per second and t is measured in seconds after the sand begins pouring. How many milliliters of sand accumulate in the bag from time t=0 to time t=2 ?

Respuesta :

MrRoyal

Answer:

35 mililiters

Step-by-step explanation:

Given

[tex]r(t) = 15t - 2t^2[/tex]

Required

Accumulated amount from t = 0 to 2

This implies that, we substitute the values of t from 0 to 2 in the function

[tex]r(0) = 15*0 - 2*0^2= 0[/tex]

[tex]r(1) = 15*1 - 2*1^2= 13[/tex]

[tex]r(2) = 15*2 - 2*2^2= 22[/tex]

The accumulated sand (r) is:

[tex]t = r(0) + r(1) + r(2)[/tex]

[tex]r = 0 + 13 + 22[/tex]

[tex]r = 35[/tex]

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