1-)The length of a rectangle is increasing at a rate of 6cm/s and its width is i
ID: 2872669 • Letter: 1
Question
1-)The length of a rectangle is increasing at a rate of 6cm/s and its width is increasing at a rate of 3cm/s. When the length is 40cm and the width is 10cm, how fast is the area of the rectangle increasing?
Answer (in cm2/s):
2-)A spherical balloon is inflated so that its volume is increasing at the rate of 2.4 ft3/min. How rapidly is the diameter of the balloon increasing when the diameter is 1.4 feet?
The diameter is increasing at ft/min.
3-)Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 5 mi2/hr. How rapidly is radius of the spill increasing when the area is 7 mi2?
The radius is increasing at mi/hr.
Explanation / Answer
1.Given dl/dt=6cm/s dw/dt=3cm/s
Area of rectangle=length * with
dA/dt=ldw/dt+wdl/dt
dA/dt=40*3+10*6=180cm^2/sec
2.Given dv/dt=2.4ft^3/min
volume of a spherical balloon=(1/6)pid^3
dv/dt=(1/2)pi.d^2.dd/dt
2.4=(1/2)pi.1.4^2.dd/dt
dd/dt=4.8/(pi*1.4*1.4)=.78 ft/min
3.Given dA/dt=5mi^2/hr
When area = 7mi^2 radius is 7/sqrt(22)
dA/dt=2pir.dr/dt
dr/dt=5/(2pi*7/sqrt(22))=.533mi/hr
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.