1) A hot metal object is submerged in cold water. The rate at which the object c

Question

1) A hot metal object is submerged in cold water. The rate at which the object cools (in degrees per minute) is a function f (t) of time. Which quantity is represented by the integral:

2) A plane travels 560 km from Los Angeles to San Francisco in 1 hour. If the plane's velocity at time t is v (t) km/h, what is the value of:

3) Which of the following quantities would be naturally represented as derivatives and which as integrals?

(a) Velocity of a train

(b) Rainfall during a 6-month period

(c) Mileage per gallon of an automobile

(d) Increase in the U.S. population from 1990 to 2010

Explanation / Answer

1)[0 to T] f(t) dt represents the change of temperature of object in T minutes

2)A plane travels 560 km from Los Angeles to San Francisco in 1 hour.

plane's velocity is constant ,v(t)=560/1 =560 km/hr

[0 to 3] v(t) dt

[0 to 3] (560) dt

=[0 to 3] (560)t

=560*(2-0)

=1680 km

[0 to 3] v(t) dt =1680km

3)

(a) Velocity of a train:represented as derivatives

(b) Rainfall during a 6-month period:represented as integrals

(c) Mileage per gallon of an automobile:represented as derivatives

(d) Increase in the U.S. population from 1990 to 2010:represented as integrals

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.