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4. Suppose you hang a bucket from a spring that stretches it 15 mm from its natural length. You then fill the bucket with different weights of sand and record the total distance stretched as recorded below Weight (N) 10 15 20 25 30 35 Distance (mm) 57.4 67.6 71.6 104.5 106.9 136.0 (a) Because the spring was stretched before the first amount of sand was added, Hooke's law predicts that the relationship between the stretched, D, and the weight of the sand, W, is DmW + 15. Create a graph of the data to test if this prediction is reasonable. If it is, use Least-square. method to estimate the value of m (b) We could also estimate the value of m by transforming the data by subtracting 15 from each distance measurement, and then fitting a straight line through the origin to the transformed data. The slope of this line is m. Do this and compare the value of m to that found in (a).

4. Suppose you hang a bucket from a spring that stretches it 15 mm from its natural length. You then fill the bucket with different weights of sand and record the total distance stretched as recorded below Weight (N) 10 15 20 25 30 35 Distance (mm) 57.4 67.6 71.6 104.5 106.9 136.0 (a) Because the spring was stretched before the first amount of sand was added, Hooke's law predicts that the relationship between the stretched, D, and the weight of the sand, W, is DmW + 15. Create a graph of the data to test if this prediction is reasonable. If it is, use Least-square. method to estimate the value of m (b) We could also estimate the value of m by transforming the data by subtracting 15 from each distance measurement, and then fitting a straight line through the origin to the transformed data. The slope of this line is m. Do this and compare the value of m to that found in (a).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
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4. Suppose you hang a bucket from a spring that stretches it 15 mm from its natural length. You then fill the bucket with different weights of sand and record the total distance stretched as recorded below |Weight (N) | 10 | 15 | 20 | 25 |Distance (mm) | 57.4 | 67.6 | 71.6 | 104.5 | 106.9 | 136.0 | 30 35 (a) Because the spring was stretched before the first amount of sand was added, Hooke's law predicts that the relationship between the stretched, D, and the weight of the sand, W, is D mW+15. Create a graph of the data to test if this prediction is reasonable. If it is, use Least-square method to estimate the value of m (b) We could also estimate the value of m by transforming the data by subtracting 15 from each distance measurement, and then fitting a straight line through the origin to the transformed data. The slope of this line is m. Do this and compare the value of m to that found in (a). 5. Find the solution of the differential equations that satisfies the given initial condition: # + 4y - 8a - 0 y-1 at z-1 6. Consider the spreading of COVID19 on an isolated South African village with population size 12 000. A portion of the population travels to nearest city for work and shopping and returns to the village infected with the disease. You would like to predict the number of the people I who will have been infected by some time t (days). Consider the following model dl 0.05/(12000 – 1) dt 7(0) = 10. (a) Solve the model for I as a function of t. (b) Determine the time Ty needed for one-third of the population to be infected.
Transcribed Image Text:4. Suppose you hang a bucket from a spring that stretches it 15 mm from its natural length. You then fill the bucket with different weights of sand and record the total distance stretched as recorded below |Weight (N) | 10 | 15 | 20 | 25 |Distance (mm) | 57.4 | 67.6 | 71.6 | 104.5 | 106.9 | 136.0 | 30 35 (a) Because the spring was stretched before the first amount of sand was added, Hooke's law predicts that the relationship between the stretched, D, and the weight of the sand, W, is D mW+15. Create a graph of the data to test if this prediction is reasonable. If it is, use Least-square method to estimate the value of m (b) We could also estimate the value of m by transforming the data by subtracting 15 from each distance measurement, and then fitting a straight line through the origin to the transformed data. The slope of this line is m. Do this and compare the value of m to that found in (a). 5. Find the solution of the differential equations that satisfies the given initial condition: # + 4y - 8a - 0 y-1 at z-1 6. Consider the spreading of COVID19 on an isolated South African village with population size 12 000. A portion of the population travels to nearest city for work and shopping and returns to the village infected with the disease. You would like to predict the number of the people I who will have been infected by some time t (days). Consider the following model dl 0.05/(12000 – 1) dt 7(0) = 10. (a) Solve the model for I as a function of t. (b) Determine the time Ty needed for one-third of the population to be infected.
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