   Chapter 5.3, Problem 14QY ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# The number of bolts B produced by a foundry changes according to the model d B d t = 250 t t 2 + 36 ,   0 ≤ t ≤ 40 where t is the time (in hours). Find the number of bolts produced in (a) 8 hours and (b) 40 hours.

(a)

To determine

To calculate: The number of bolts B produce in 8 hours that is changes according to the model dBdt=250tt2+36, 0t40.

Explanation

Given Information:

The number of bolts B produced by a foundry changes according to the model given by below

dBdt=250tt2+36, 0t40

Where time (in hours) is t.

Formula used:

The power rule of integrals:

undu=un+1n+1+C (for n1)

Here, u is function of x.

The property of Intro-differential:

df(x)dxdx=f(x)

Calculation:

The first derivative of function f(x):

dBdt=250tt2+36

Apply, integration on both sides with respect t for limit 0t8:

08dBdtdt=08(250tt2+36)dt=12508((

(b)

To determine

To calculate: The number of bolts B produce in 40 hours that is changes according to the model dBdt=250tt2+36, 0t40.

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