Find the equation y = Po + B,x of the least-squares line that best fits the given data points. (4,3), (5,2), (7,1), (8,0) The line is y =O+ ()x. (Type integers or decimals.)

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Find the equation y = Bo + B,x of the least-squares line that best fits the given data points.
(4,3), (5,2), (7,1), (8,0)
The line is y =+ (Ox.
(Type integers or decimals.)
Transcribed Image Text:Find the equation y = Bo + B,x of the least-squares line that best fits the given data points. (4,3), (5,2), (7,1), (8,0) The line is y =+ (Ox. (Type integers or decimals.)
According to Kepler's first law, a comet should have an elliptic, parabolic, or hyperbolic orbit (with gravitational attractions from the planets ignored). In suitable polar coordinates, the position (r, 9) of a
comet satisfies an equation of the form r= B+ e(r• cos 9), where B is a constant and e is the eccentricity of the orbit, with 0se<1 for an ellipse, e = 1 for a parabola, and e>1 for a hyperbola. Suppose
observations of a newly discovered comet provide the data below. Determine the type of orbit, and predict where the comet will be when 9 = 4.3 (radians).
0.86
1.06
1.48
1.78
2.14
3.51
3.14
2.08
0.94
0.62
The comet has a hyperbolic orbit.
When 9 = 4.3 (radians), the comet will be at r =
(Round to two decimal places as needed.)
Transcribed Image Text:According to Kepler's first law, a comet should have an elliptic, parabolic, or hyperbolic orbit (with gravitational attractions from the planets ignored). In suitable polar coordinates, the position (r, 9) of a comet satisfies an equation of the form r= B+ e(r• cos 9), where B is a constant and e is the eccentricity of the orbit, with 0se<1 for an ellipse, e = 1 for a parabola, and e>1 for a hyperbola. Suppose observations of a newly discovered comet provide the data below. Determine the type of orbit, and predict where the comet will be when 9 = 4.3 (radians). 0.86 1.06 1.48 1.78 2.14 3.51 3.14 2.08 0.94 0.62 The comet has a hyperbolic orbit. When 9 = 4.3 (radians), the comet will be at r = (Round to two decimal places as needed.)
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