The velocity (in centimeters per second) of blood molecules flowing through a capillary of radius 0.008 cm is v = 6.4 × 10−8 − 0.001r2, where r is the distance from the molecule to the center of the capillary. Find the rate of change of velocity with respect to r when r = 0.004 cm.

The velocity (in centimeters per second) of blood molecules flowing through a capillary of radius 0.008 cm is v = 6.4 × 10−8 − 0.001r2, where r is the distance from the molecule to the center of the capillary. Find the rate of change of velocity with respect to r when r = 0.004 cm.

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter2: Working With Real Numbers

Section2.3: Rules For Addition

Problem 14P

See similar textbooks

Related questions

Q: Find the average velocity for the position function , in mm, over the interval , where is in…

A: Here I am attaching image so that you understand each and every step.

Q: A balloon is being inflated. If its volume increases at the rate of 5cm^3/sec, how fast is the…

Q: The length of a rectangle is given by 2t + 5 and its height is Vt, where t is time in seconds and…

A: In the given question the length and height of the rectangle are given: The area of the rectangle…

Q: James is pumping air into a spherical balloon at a rate of : бст3 What is the rate of change of the…

A: Find the rate of change in the question by doing the derivative with respect to time after…

Q: Describe the change in accuracy of dz as an approximation of ∆z as ∆x and ∆y increase.

A: Given , z=fx,yWe do dz using the partial derivates zx & zy .So , dz=zx.dx & zy.dywhere zx…

Q: A man whose height is 1.5 m. is walking directly away from a lamp post at a constant rate of 0.8…

Q: If a ball of candy is covered in chocolate and is melting so that its surface area decreases at a…

A: To find: The rate at which diameter decreases when diameter is 10 cm. Given: The rate of surface…

Q: The altitude (,) of a right circular cylinder is always equal to the diameter (a) of the base. Find…

Q: A hot-air balloon is 190 ftabove the ground when a motorcycle (traveling in a straight line on a…

A: Let x be the horizontal distance from balloon to motorcycle, y be the vertical distance from the…

Q: Assuming there is no sag in the string, find the rate at which the kite is moving when 125

A: Considering a right triangle with the data given, the hypotenuse 'c' is 125 feet, base 'b' and the…

Q: The surface area of a sphere increases at a rate of 55 m²/sec. Then the rate at which the radius…

Q: A spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute. (a) Find…

A: Given: Rate of change of volume of spherical balloon is dVdt=800cm3/min. (a) To find: Rate of change…

Q: What is the velocity (in ft/s) of a sandbag 2.5 s after it is released from a hot-air balloon that…

A: Given that a sandbag is released from a hot-air balloon that is stationary in the air. Then we have…

Q: What is the rate of change of the volume of a ball (V = (4/3)πr3) with respect to the radius when…

A: Given: volume v=43πr3 for finding rate of change of volume with respect to radius r, we…

Q: Assume a circle is expanding with time, where r = t + 2. What is the formula for the rate of change…

A: Given: r = t + 2 We know that the area of the circle: A = π r2 where r is radius.

Q: What is the rate of change of the volumeof a ball (V = (4>3)pr3) with respect to the radius…

A: The volume of a ball with radius r is given by V=43πr3 Recall that the rate of change is given by…

Q: A balloon, in the shape of a right circular cylinder, is being inflated in such a way that the…

Q: An oil tanker aground on a reef is forming a circular oil slick about 0.1 foot thick. If the oil was…

A: Given that An oil tanker aground on a reef is forming a circular oil slick about 0.1 foot thick. If…

Q: A spherical balloon is expanding. If the radius is increasing at the rate of 2 inches per minute, t…

Q: Water is flowing into an inverted conical reservoir, 20 ft deep and 10 ft across the top, at the…

Q: A rocket lifts off the surface of Earth with a constant acceleration of 20 m/sec2. How fast will the…

Q: Find the surface area of a sphere at the instant when the rate of increase of the volume of the…

Q: A spherical balloon is inflated with gas at the rateof 800 cubic centimeters per minute. (b) Explain…

A: To find the rate of change of the radius, differentiate the volume of the sphere, V=43πr2 with…

Q: A 12-foot ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder…

A: A 12-foot ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder…

Q: The volume V of a right circular cone of radius r and height h is given by V = 1/3 πr2h. a) What is…

A: Simply take derivative with respect to given variable considering other as constant.

Q: 15. Gas is being pumped into a spherical balloon at the rate of 10 cubic inches per second. When the…

A: NOTE: Refresh your page if you can't see any equations. . here we have the diameter is 30 inches so…

Q: The width of a rectangle is increasing at a rate of 2cm/sec, while the length increases at 3cm/sec.…

Q: A balloon has just been inflated. Calculate the instantaneous rate of change by which the area…

A: Introduction: A geometric shape with a sphere-like appearance. In three dimensions, the sphere is…

Q: The legs of an isosceles right triangle increase in length at a rate of 6 m divided by s.a. At what…

A: Let x be the length of leg and h be the length of hypotenuse of an isosceles right triangle. Then…

Q: A Fluid flows in an inverted conical tank, 14 in diameter on top and 24in deep at a rate of…

Q: The hour hand of a clock is 4 inches long and the minute hand is 6 inches long. At the moment the…

A: The hour hand of clock is 4 inches long and the minute hand is 6 inches long. At that time angle…

Q: The surface area of a sphere, initially zero, increases uniformly at 4 square inches pe second. Find…

A: Since you have asked multiple questions here, we will solve the first question for you. To get the…

Q: A spherical snowball melts at a rate of 2 cubic centimeters per hour. How fast is the radius…

A: We know that the volume of a spherical snowball is v = 43πr3 where v is the volume and r is the…

Q: A pebble is dropped into a calm pond, causing ripples in the form of concentric circles, as shown.…

Q: A yellow balloon, spherical in shape is inflated with a rate of 100 cm3 /sec. Calculate the rate at…

A: Given

Q: The radius r and height h of a cylinder are changing with time. At the instant in question, r = 4…

A: Given problem:- The radius r and height h of a cylinder are changing with time. At the instant in…

Q: A 50 – gal tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1 lb…

A: Remaining capacity of tank is 50-10 = 40 gallons.

Q: ) A snowball is melting at a rate of 1 cm3 per second. If it remains spherical, how fast is the…

Q: A balloon leaving the ground 60 ft. from an observer, rises vertically at the rate of 10 ft. per…

Q: Find the rate of change of the surface area of a hemisphere with respect to its radius. a. When the…

Q: The surface area of a balloon that is being filled with helium increases at a rate of 5 square feet…

Q: A hot air balloon is 120 ft. above the ground when a motorcycle (travleing in a straight line on a…

A: Given that, A hot air balloon is 120 ft. above the ground when a motorcycle (traveling in a straight…

Q: The tempature at any point on a cordinate plane is T=3x2+4y2+5. What is the rate of change from the…

A: Note: We know that, We need to find the rate of change from the origin, considering it's the same…

Q: A man walks along a straight path of 4m/s. A searchlight is located on the ground 25m from the path…

Q: Water is drained from a pool at a rate of R(t) = 50e-0.08t gallons per hour. If the drain is left…

A: 625 gal. water drains from the pool.

Q: A spherical balloon is inflated at a rate of 21 cm's1. Find the rate of change of the surface when…

A: Volume (V) of the sphere = (4/3) pi r3 Surface area (S) of the sphere = 4 pi r2 where r is the…

Q: The diameter of a spherical balloon that is being filled with air is increasing at the rate of 3…

A: the volume of the sphere is given by ..............(1)

Q: A baseball thrown directly upward at 160 ft/sec has velocity v(t) = 160- 32t ft/sec at time t…

Question

The velocity (in centimeters per second) of blood molecules flowing through a capillary of radius 0.008 cm is v = 6.4 × 10⁻⁸ − 0.001r², where r is the distance from the molecule to the center of the capillary. Find the rate of change of velocity with respect to r when r = 0.004 cm.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Chain Rule$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Algebra: Structure And Method, Book 1

Algebra

ISBN:

9780395977224

Author:

Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:

McDougal Littell