ed to obtain water flow speed u in m/s at different time steps / in minutes. For the four data points, presented in the following table, obtained from the test i 1 2 3 4 Time (t) Speed (v) 0.5 0.98 1.5 2.98 2.5 8.78 3.5 15.18 the following quadratic model (equation) is chosen to fit the experimental points y(x) = a₁x + ₂x² (a) The following system of equations is used to calculate the regression coefficients a₁ and 2:
ed to obtain water flow speed u in m/s at different time steps / in minutes. For the four data points, presented in the following table, obtained from the test i 1 2 3 4 Time (t) Speed (v) 0.5 0.98 1.5 2.98 2.5 8.78 3.5 15.18 the following quadratic model (equation) is chosen to fit the experimental points y(x) = a₁x + ₂x² (a) The following system of equations is used to calculate the regression coefficients a₁ and 2:
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
Related questions
Question
Please provide 3 sig. digits and DO NOT approximate numbers for intermediate steps
![A test is conducted to obtain water flow speed u in m/s at different time steps t in minutes. For the four data points,
presented in the following table, obtained from the test
i
1
2
3
4
Time (t) Speed (v)
0.5
0.98
1.5
2.98
2.5
8.78
3.5
15.18
the following quadratic model (equation) is chosen to fit the experimental points y(x) = a₁x + ₂x²
(a) The following system of equations is used to calculate the regression coefficients a1 and 42:
n
Σ fi(xi)fi(xi) [f1(x;)ƒ2(x;)
i=1
n
Σ f2(xi)f1(xi)
i=1
i=1
194.25
(2)-(2)
=
247.78
a1
a2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4ac6c15-8cf8-41f0-a03d-1b63fab71194%2F7280fe05-9560-4073-96ea-a212e9081f40%2Ffi90sxh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A test is conducted to obtain water flow speed u in m/s at different time steps t in minutes. For the four data points,
presented in the following table, obtained from the test
i
1
2
3
4
Time (t) Speed (v)
0.5
0.98
1.5
2.98
2.5
8.78
3.5
15.18
the following quadratic model (equation) is chosen to fit the experimental points y(x) = a₁x + ₂x²
(a) The following system of equations is used to calculate the regression coefficients a1 and 42:
n
Σ fi(xi)fi(xi) [f1(x;)ƒ2(x;)
i=1
n
Σ f2(xi)f1(xi)
i=1
i=1
194.25
(2)-(2)
=
247.78
a1
a2
![Calculate the following values:
P
Σ f1(x;)ƒ1(x;) =
i=1
Σ ƒ1(x;)ƒ2(x;) =
Σ f2(x)f(x) =
i=1
PL
Σ yifi(x) =
i=1
(b) Solve the above system of equations to obtain the nonlinear equation coefficients a₁ and ₂:
a1 =
a2 =
(c) Find the predicted value of the speed u at t = 3 (-
v(3) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4ac6c15-8cf8-41f0-a03d-1b63fab71194%2F7280fe05-9560-4073-96ea-a212e9081f40%2Foh7ao4b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Calculate the following values:
P
Σ f1(x;)ƒ1(x;) =
i=1
Σ ƒ1(x;)ƒ2(x;) =
Σ f2(x)f(x) =
i=1
PL
Σ yifi(x) =
i=1
(b) Solve the above system of equations to obtain the nonlinear equation coefficients a₁ and ₂:
a1 =
a2 =
(c) Find the predicted value of the speed u at t = 3 (-
v(3) =
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