Mathematics: Please help what is the equivalent expression of 1/4(2-5x+6)

Please help what is the equivalent expression of

Ответ:

xDoxing

19.04.2022

Mathematics

a) $V(r) = \int\limits^5_00.114e^{-1.8r} \, dr$

b) V = 0.0629

Step-by-step explanation:

We have that the depth, in millimeters, of the soot deposited each month at a distance r kilometers from the incinerator is given by:

$H(r) = 0.114e^{-1.8r}$

(a) Write a definite integral (with independent variable r) giving the total volume of soot deposited within 5 kilometers of the incinerator each month.

This is the integral of H(r) with r varying from 0 to 5. So:

$V(r) = \int\limits^5_0H(r) \, dr$

$V(r) = \int\limits^5_00.114e^{-1.8r} \, dr$

(b) Evaluate the integral you found in part (a) to find the volume of soot.

$V(r) = \int\limits^5_00.114e^{-1.8r} \, dr$

$V(r) = 0.114\int\limits^5_0e^{-1.8r} \, dr$

$V(r) = -\frac{0.114}{1.8}e^{-1.8r}, 0\leq r\leq5$

$V(r) = -0.063e^{-1.8r}, 0\leq r\leq5$

V = V(5) - V(0)

V = -0.00000777481 - (-0.063)

V = 0.0629

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Please help what is the equivalent expression of 1/4(2-5x+6)

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