Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Time (s) Volume (cm³) 0 0 30 5.0 60 10.2 90 14.8 120 19.9 150 25.1 180 30.2 Questions: 1. Analyze the data. Was the rate of change of volume with respect to time constant? Justify your answer and explain the results. 2. Determine the initial volume of sand and write an equation for the volume of sand remaining in the cone after t seconds. 3. Rearrange the formula V = r²h to solve or the depth. In order to get an equation for the depth as a function of volume, you must substitute for r in terms of h. This can be done using similar triangles as shown below. The ratio of the radius and the depth (height) is always constant regardless of the volume of and in the cone. In the diagram, r represents the radius of the surface of the sand and h represents the depth. The variable R represents the radius the cone and H represents the height of the cone.

Time (s) Volume (cm³) 0 0 30 5.0 60 10.2 90 14.8 120 19.9 150 25.1 180 30.2 Questions: 1. Analyze the data. Was the rate of change of volume with respect to time constant? Justify your answer and explain the results. 2. Determine the initial volume of sand and write an equation for the volume of sand remaining in the cone after t seconds. 3. Rearrange the formula V = r²h to solve or the depth. In order to get an equation for the depth as a function of volume, you must substitute for r in terms of h. This can be done using similar triangles as shown below. The ratio of the radius and the depth (height) is always constant regardless of the volume of and in the cone. In the diagram, r represents the radius of the surface of the sand and h represents the depth. The variable R represents the radius the cone and H represents the height of the cone.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

I posted the same question. In case, since I'm asking for more than one questjkn

start from q2 and answer as many

SE Time (s) Volume (cm) 0 0 30 5.0 60 10.2 90 14.8 120 19.9 150 25.1 180 30.2 Questions: 1. Analyze the data. Was the rate of change of volume with respect to time constant? Justify your answer and explain the results. 2. Determine the initial volume of sand and write an equation for the volume of sand remaining in the cone after t seconds. 3. Rearrange the formula V = r²h to solve or the depth. In order to get an equation for the depth as a function of volume, you must substitute for r in terms of h. This can be done using similar triangles as shown below. The ratio of the radius and the depth (height) is always constant regardless of the volume of and in the cone. In the diagram, r represents the radius of the surface of the sand and h represents the depth. The variable R represents the radius of the cone and H represents the height of the cone. H Vi h R Rh == ² :. r = Substitute the values for R and H and simplify to get an expression for r. Use this to replace r in the equation for depth and simplify. This results in a formula for depth as a function of volume only. 4. Substitute the volume in terms of time in your formula from step 2 to obtain an equation for the depth as a function of time. 5. Determine the rate of change of depth with respect to time using your model from step 4. 6. Determine the rate of change of depth with respect to time after 120 s using your model from step 4. While sand was leaking out of the cone, data was recorded every 30 s to measure the depth of the sand inside the cone filter. These values are shown in the table below. Time (s) Level of Sand (cm) 0 6.0 30 5.8 60 5.6 90 5.4 120 5.1 4.8 150 180 4.4 7. Did the level of sand in the cone decrease at a constant rate? Justify your answer and explain. 8. Create a graph of the sand level versus time. Draw a line or curve of best fit and determine the rate at which the level of sand was changing after 120 s. 9. Compare your answer from step 8 to the value obtained in step 6. Explain the results.
Transcribed Image Text:SE Time (s) Volume (cm) 0 0 30 5.0 60 10.2 90 14.8 120 19.9 150 25.1 180 30.2 Questions: 1. Analyze the data. Was the rate of change of volume with respect to time constant? Justify your answer and explain the results. 2. Determine the initial volume of sand and write an equation for the volume of sand remaining in the cone after t seconds. 3. Rearrange the formula V = r²h to solve or the depth. In order to get an equation for the depth as a function of volume, you must substitute for r in terms of h. This can be done using similar triangles as shown below. The ratio of the radius and the depth (height) is always constant regardless of the volume of and in the cone. In the diagram, r represents the radius of the surface of the sand and h represents the depth. The variable R represents the radius of the cone and H represents the height of the cone. H Vi h R Rh == ² :. r = Substitute the values for R and H and simplify to get an expression for r. Use this to replace r in the equation for depth and simplify. This results in a formula for depth as a function of volume only. 4. Substitute the volume in terms of time in your formula from step 2 to obtain an equation for the depth as a function of time. 5. Determine the rate of change of depth with respect to time using your model from step 4. 6. Determine the rate of change of depth with respect to time after 120 s using your model from step 4. While sand was leaking out of the cone, data was recorded every 30 s to measure the depth of the sand inside the cone filter. These values are shown in the table below. Time (s) Level of Sand (cm) 0 6.0 30 5.8 60 5.6 90 5.4 120 5.1 4.8 150 180 4.4 7. Did the level of sand in the cone decrease at a constant rate? Justify your answer and explain. 8. Create a graph of the sand level versus time. Draw a line or curve of best fit and determine the rate at which the level of sand was changing after 120 s. 9. Compare your answer from step 8 to the value obtained in step 6. Explain the results.
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS