For the following exercises, assume an object enters our solar system and we want to graph its path on a
70. The object enters along a path approximated by the line
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- 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=0.5x+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=0.5x2 .arrow_forwardFor 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. 67. The object enters along a path approximated by the line y=2x2 and passes within 0.5 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=2x+2 .arrow_forwardFor the following exercises, find the equation of the line with the given information. 17. Passes through the point (2,1) and is perpendicular to y=25x+3 .arrow_forward
- For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, orneither parallel nor perpendicular: Find the area of a triangle bounded by the y-axis,the line f(x)=124x, and the lineperpendicularto f that passes through the origin.arrow_forwardFor the following exercises, use your graphing calculator to input the linear graphs in the Y= graph menu. After graphing it, use the 2ndCALC button and 2:zero button, hit ENTER. At the lower part of the screen you will see “left bound?” and a blinking cursor on the graph of the line. Move this cursor to the left of the x-intercept, hit ENTER. Now it says “right bound?" Move the cursor to the right of the x-intercept, hit ENTER. Now it says “guess?” Move your cursor to the left somewhere in between the left and right bound near the x-intercept. Hit ENTER. At the bottom of your screen it will display the coordinates of the x-intercept or the “zero" to the y-value. Use this to find the x-intercept. Note: With linear/straight line functions the zero is not really a “guess,” but it is necessary to enter a “guess” so it will search and find the exact x-intercept between your right and left boundaries. With other types of functions (more than onex-intercept), they may be irrational numbers so “guess” is more appropriate to give it the correct limits to find a very close approximation between the left and right boundaries. 52.Y1=4x7arrow_forwardFor the following exercises, use your graphing calculator to input the linear graphs in the Y= graph menu. After graphing it, use the 2ndCALC button and 2:zero button, hit ENTER. At the lower part of the screen you will see “left bound?” and a blinking cursor on the graph of the line. Move this cursor to the left of the x-intercept, hit ENTER. Now it says “right bound?" Move the cursor to the right of the x-intercept, hit ENTER. Now it says “guess?” Move your cursor to the left somewhere in between the left and right bound near the x-intercept. Hit ENTER. At the bottom of your screen it will display the coordinates of the x-intercept or the “zero" to the y-value. Use this to find the x-intercept. Note: With linear/straight line functions the zero is not really a “guess,” but it is necessary to enter a “guess” so it will search and find the exact x-intercept between your right and left boundaries. With other types of functions (more than onex-intercept), they may be irrational numbers so “guess” is more appropriate to give it the correct limits to find a very close approximation between the left and right boundaries. 53.Y1=3x+54 Round your answer to the nearest thousandth.arrow_forward
- For the following exercises, use your graphing calculator to input the linear graphs in the Y= graph menu. After graphing it, use the 2ndCALC button and 2:zero button, hit ENTER. At the lower part of the screen you will see “left bound?” and a blinking cursor on the graph of the line. Move this cursor to the left of the x-intercept, hit ENTER. Now it says “right bound?" Move the cursor to the right of the x-intercept, hit ENTER. Now it says “guess?” Move your cursor to the left somewhere in between the left and right bound near the x-intercept. Hit ENTER. At the bottom of your screen it will display the coordinates of the x-intercept or the “zero" to the y-value. Use this to find the x-intercept. Note: With linear/straight line functions the zero is not really a “guess,” but it is necessary to enter a “guess” so it will search and find the exact x-intercept between your right and left boundaries. With other types of functions (more than onex-intercept), they may be irrational numbers so “guess” is more appropriate to give it the correct limits to find a very close approximation between the left and right boundaries. 51.Y1=8x+6arrow_forwardFor the following exercises, find the equation of the line with the given information. 15. Passes through the points (4,2)and(5,3).arrow_forwardFor each of the following exercises, identify the information requested. 27. What are the coordinates of the origin?arrow_forward
- For the following exercises, find the equation of the line using the given information. 30. (2,0)and(2,5)arrow_forwardFor each of the following exercises, use the graph in the figure below. 47.Which point is closer to the origin?arrow_forwardFor the following exercises, find the equation of the line using the given information. 35. (1,3)and(4,5)arrow_forward