What is the rate of change of the area of

Josh Sizemore 2021-12-24 Answered
What is the rate of change of the area of a circle with respect to the radius when the radius is r = 3 in.?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Virginia Palmer
Answered 2021-12-25 Author has 27 answers
The area of a circle is given as
A(r)=πr2
To find the instantneous rate of change with respect to r, we apply the slope formula:
limh0π(r+h)2πr2h=limh0π(r2+2hr+h2)πr2h
=limh0π(2hr+h2)h
=limh0πh(2r+h)h
=limh0[π(2r+h)]
Substitute r=3:
=limh0[π(6+h)]
=6π
When the radius is 3 in., area is changing at a rate of 6π
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2020-12-24
Water stands at a depth H in a large, open tank whose sidewalls are vertical. A hole is made in one of the walls at a depth h below the water surface.
a) at what distance R from the foot of the wall does the emerging stream strike the floor?
b) How far above the bottom of the tank could a second hole be cut so that the stream emerging from it could have the same range as for the first hole?
asked 2021-02-26
A tow truck pulls a car that is stuck in the mud, with a force of 2500 N as in Fig P5.27 The tow cable is under tension and therefor pulls downward and to the left on the pin at its upper end. The light pin is held in equilibrium by forces exerted by the two bars A and B. Each bar is a strut that is, each is a bar whose weight is small compared to the forces it exerts, and which exerts forces only through hinge pins at its ends. Each strut exerts a force directed parallel to its length. Determine the force of tension or compression in each strut. Proceed as follows Make a guess as to which way (pushing or pulling ) each force acts on the top pin Draw a free-body diagram of the pin. Use the condition for equilibrium of the pin to translate the free-body diagram into equations. From the equations calculate the forces exerted by struts A and B. If you obtain a positive answer, you correctly guessed the direction of the force. A negative answer means the direction should be reversed, but the absolute value correction should be reversed, but the absolute value correctly gives the magnitude of the force. If a strut pulls of a pin, it is in tension. If it pushes, the strut is in compression. Identify whether each strut is in tension or in compression.
asked 2021-02-09

In Figure, a stationary block explodes into two pieces and R that slide across a frictionless floor and then into regions with friction, where they stop. Piece L, with a mass of 2.6 kg, encounters a coefficient of kinetic friction μL=0.40 and slides to a stop in distance deal = 0.15 m. Piece R encounters a coefficient of kinetic friction μR=0.50 and slides to a stop in distanced R=0.30 m. What was the mass of the original block?
image

asked 2020-12-05
A 5.00kg sack of flour is lifted vertically at a constant speed of 3.50m/s through a height of 15.0m. a) How great a force is required? b) How much work is done on the sack by the lifting force? What becomes of this work?
asked 2021-02-12
Find the similarity ratio of two triangles with areas 81feet2and100feet2.
asked 2022-05-30
Prove that 1 2 + k = 1 n cos ( k x ) = sin ( n + 1 2 ) x 2 sin ( 1 2 x ) for any x R
asked 2022-02-11
How do you find the equation of a tangent line to a curve?

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question