For the following exercises, assume an object enters our solar system and we want to graph its path on a coordinate system with the sun at the origin and the x -axis as the axis of symmetry for the objects path. Give the equation of the flight path of each object using the given information. 68. The object enters along a path approximated by the line y = 0.5 x + 2 and passes within 1 au of the sun at its closest approach, so the sun is one focus of the hyperbola. It then departs the solar system along a path approximated by the line y = − 0.5 x − 2 .
For the following exercises, assume an object enters our solar system and we want to graph its path on a coordinate system with the sun at the origin and the x -axis as the axis of symmetry for the objects path. Give the equation of the flight path of each object using the given information. 68. The object enters along a path approximated by the line y = 0.5 x + 2 and passes within 1 au of the sun at its closest approach, so the sun is one focus of the hyperbola. It then departs the solar system along a path approximated by the line y = − 0.5 x − 2 .
For the following exercises, assume an object enters our solar system and we want to graph its path on a coordinate system with the sun at the origin and the x-axis as the axis of symmetry for the objects path. Give the equation of the flight path of each object using the given information.
68. The object enters along a path approximated by the line
y
=
0.5
x
+
2
and passes within 1 au of the sun at its closest approach, so the sun is one focus of the hyperbola. It then departs the solar system along a path approximated by the line
y
=
−
0.5
x
−
2
.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
ANSWER EVERY SINGLE QUESTION FROM BOTH THE PICTURE AND FROM WHAT I HAVE WRITTEN BELOW PLEASE! Please answer every single question from both the picture and what I have written down below and only use the numbers I have provided when answering.
Answer my questions from the picture then continue below.
#2.) Determine whether the graph of the equation is symmetric with respect to the x-axis and y-axis
X=2y² - 4
Answers:
A.) X-axis= yes or no?
B.) Y-axis= yes or no?
Question #3.) Determine whether the graph of the equation is symmetric with respect to the x-axis and y-axis.
X² - y²=14
Answers: X-axis= yes or no?
Y-axis= yes or no?
Question #4.) Find (g○f)(x) and (f○g)(x) for the given functions f and g
F(x)=4x+5, g(x)=2x-9
Answers: (g○f)(x)=
(F○g)(x)=
Question #5.) evaluate the composite function, where f(x)=2x+4, g(x)=x²-5x, and h(x)=4-3x²
(G○f)(2)
Answer:
Write the equation of the height of a rider on each of the following Ferris wheels t seconds after the
rider passes the farthest right position.
a. The radius of the wheel is 30 feet, the center of the wheel is 45 feet above the ground, and the
angular speed of the wheel is 15 degrees per second counterclockwise.
Equation:
b. Sketch the graph below.
40
-35
30-
-25
-20-
-15
10-
Time (seconds)
Height (feet)
A chicken coop has been built 30 yards south of a farmhouse and is enclosed by a circular fence. Following a linear path that joins the farmhouse to the chicken coop, you must travel 24 yards before arriving at the fence. With the farmhouse as the origin and the positive x- and y-axes oriented east and north, respectively, what is the equation of the circular fence?
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