In September 2009, Australian astronomer Robert H.McNaught discovered comet C/2009 R 1 (McNaught). The orbit of this comet is hyperbolic with the Sun at one focus. Because the orbit is not elliptical, the comet will not be captured by the Sun's gravitational pull and instead will pass by the Sun only once. The comet reached perihelion on July 2, 2010 The path of comet can be modeled by the equation x 2 1191.2 2 − y 2 30.9 2 = 1 where x and y are measured in AU (astronomical units). a. Determine the distance (in AU) at perihelion. Round to 1 decimal place. b. Using the rounded value from part (a), if 1 AU≈93,000,000 mi, find the distance in miles.
In September 2009, Australian astronomer Robert H.McNaught discovered comet C/2009 R 1 (McNaught). The orbit of this comet is hyperbolic with the Sun at one focus. Because the orbit is not elliptical, the comet will not be captured by the Sun's gravitational pull and instead will pass by the Sun only once. The comet reached perihelion on July 2, 2010 The path of comet can be modeled by the equation x 2 1191.2 2 − y 2 30.9 2 = 1 where x and y are measured in AU (astronomical units). a. Determine the distance (in AU) at perihelion. Round to 1 decimal place. b. Using the rounded value from part (a), if 1 AU≈93,000,000 mi, find the distance in miles.
Solution Summary: The author calculates the distance (in AU) at perihelion when the path of the comet can be modeled by the equation.
In September 2009, Australian astronomer Robert H.McNaught discovered comet C/2009
R
1
(McNaught). The orbit of this comet is hyperbolic with the Sun at one focus. Because the orbit is not elliptical, the comet will not be captured by the Sun's gravitational pull and instead will pass by the Sun only once. The comet reached perihelion on July 2, 2010 The path of comet can be modeled by the equation
x
2
1191.2
2
−
y
2
30.9
2
=
1
where x and y are measured in AU (astronomical units).
a. Determine the distance (in AU) at perihelion. Round to 1 decimal place.
b. Using the rounded value from part (a), if 1 AU≈93,000,000 mi, find the distance in miles.
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
Find the exact area inside r=2sin(2\theta ) and outside r=\sqrt(3)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.