Rate of Change of Volume and Diameter of a Tree, Acceleration and Velocity Functions

According to the Doyle log rule , the volume V in broad feet of a log of length L (feet) and diameter D (inches) at the small end is

V= (D-4/4)^2 *L

Find the rate at which the volume is changing with respect to D for a 12-foot long log whose smallest diameter is a.) 8 inches, b.) 16 inches, c.) 24 inches, and d.) 36 inches.

The position function of a particle is given by s= 1/ t^2 + 2t + t
where s is the height in feet and t is the time in seconds.
Find the velocity and acceleration functions

Solution Summary

The Rate of Change of Volume and Diameter of a Tree and Acceleration and Velocity Functions are investigated.

I need writing a program to calculate the volume flow rate in cubic feet per second of water flowing through a pipe of diameter d in inches and a velocity of v feet per second. The formula for the flow rate is given by
Q = area * velocity
Where area= πd² /4 in square feet.

Compute the volume of water in cubic feet, flowing through a pipe of diameter d in feet, with a velocity of v feet per second. The formula to compute the volume flow rate per second is given by:
R = d /2
Area= π . r^2
Volume = area .v

See attached data file.
BC LUMBER harvests trees throughout the U.S. and Canada. They need to be able to estimate the amount of timber in a given area of forest. More specifically they need a quick and easy way to determine the volume of any given tree. Unfortunately, it is difficult to measure the volume of a tree directly.

See attached file for full problem description.
Acceleration:
1. A car goes from rest to 60 ft/sec in 30 seconds, what was its average acceleration?
2. A rocket accelerates at a rate of 200 m/sec^2 from rest for 20 seconds. What is its final velocity?
3. If the total change in velocity of an object was 50 m/sec for 10 seco

1. A particle oscillates between the points x = 40 mm and x = 160 mm with an acceleration a = k( 100 - x), where a and x are expressed in mm/ s^2 and mm, respectively, and k is a constant. The velocity of the particle is 18 mm/ s when x = 100 mm and is zero at both x = 40 mm and x = 160 mm. Determine (a) the value of k,( b) the

BC LUMBER is trying to obtain a better prediction on the volume of its trees. A
sample of trees of various diameters were cut and the diameters, heights andvolumes were recorded. The results are given below.
DIAMETER: Diameter in inches at 4.5 feet above ground level
HEIGHT: Height of the tree in feet
VOLUME: Volume

A 1.2ft diameter ball is thrown onto a rough surface, such that it has a velocity of 6ft/s and a backspin angular velocity of w. If it is to stop backspinning at the same instant as the velocity is 0, the backspin w in rad/s is what? HINT: The answer is independent of the mass and coefficient of friction.
a. 17.8
b. 22.0
c. 2

Find 3rd derivative
f(x)= 3/16x^2
Find the indicated value
f(x)= 9-x^2 value f''(-sq rt 5)
Find f'''(x)
f''(x)=2x-2/x
Find the second derivative and solve the equationf''(x)=0
f(x)=x/x^2+1
The velocity of an object in meters per second is
v(t)=36-t, 0velocity andacceleration of the

Please help answer the following questions. Provide step by step calculations for each.
It has been argued that power plants should make use of off-peak hours (such as late at night) to generate mechanical energy and store it until it is needed during peak load times, such as the middle of the day. One suggestion has been to