8. Q8
Save videos to My Cheatsheet for later, for easy studying.
Video Solution
Q1
Q2
Q3
L1
L2
L3
Similar Question 1
<p>Part of the path of an asteroid is approximately parabolic and is modelled by the function <code class='latex inline'>y = -6x^2 - 370x + 100 900</code>. For the period of time that it is in the same area, a space probe is moving along a straight path on the same plane as the asteroid according to the linear equation <code class='latex inline'>y = 500x-83024</code>. A space agency needs to determine if the asteroid will be an issue for the space probe. Will the two paths intersect? Show your work.</p>
Similar Question 2
<p>Part of the path of an asteroid is approximately parabolic and is modelled by the function <code class='latex inline'>y = -6x^2 - 370x + 100 900</code>. For the period of time that it is in the same area, a space probe is moving along a straight path on the same plane as the asteroid according to the linear equation <code class='latex inline'>y = 500x-83024</code>. A space agency needs to determine if the asteroid will be an issue for the space probe. Will the two paths intersect? Show your work.</p>
Similar Question 3
<p>Andrea&#39;s supervisor at the actuarial firm has asked her to determine the safety zone needed for a fireworks display. She needs to find out where the safety fence needs to be placed on a hill. The fireworks are to be launched from a platform at the base of the hill. Using the top of the launch platform as the origin and taking some measurements, in metres, Andrea comes up with the following equations.</p><p>Cross-section of the slope of one side of the hill: <code class='latex inline'>y = -4x -12</code></p><p>Path of the fireworks: <code class='latex inline'>y = -x^2 + 15x</code></p><p><strong>(a)</strong> Illustrate this situation by graphing both equations on the same set of axes.</p><p><strong>(b)</strong> Calculate the coordinates of the point where the function that describes the path of the fireworks will intersect the equation for the hill.</p>
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>The revenue function for a production by a theater group is given by <code class='latex inline'>R(t) = -50t^2 + 300t</code>, where <code class='latex inline'>t</code> is the ticket price. The cost function for the production is given by the function <code class='latex inline'>C(t) = 600-50t</code>. Determine the ticket price(s) that must be sold that will allow the production to break even.</p>
<p>The path of an underground stream is given by the function <code class='latex inline'>y = 4x^2 + 17x- 32</code>. Two new houses need wells to be dug. On the area plan, these houses lie on a line defined by the equation <code class='latex inline'>y = -15x + 100</code>. Determine the coordinates where the two new wells should be dug.</p>
<p>Andrea&#39;s supervisor at the actuarial firm has asked her to determine the safety zone needed for a fireworks display. She needs to find out where the safety fence needs to be placed on a hill. The fireworks are to be launched from a platform at the base of the hill. Using the top of the launch platform as the origin and taking some measurements, in metres, Andrea comes up with the following equations.</p><p>Cross-section of the slope of one side of the hill: <code class='latex inline'>y = -4x -12</code></p><p>Path of the fireworks: <code class='latex inline'>y = -x^2 + 15x</code></p><p><strong>(a)</strong> Illustrate this situation by graphing both equations on the same set of axes.</p><p><strong>(b)</strong> Calculate the coordinates of the point where the function that describes the path of the fireworks will intersect the equation for the hill.</p>
<p>A parachutist jumps from an airplane and immediately opens his parachute. His altitude, <code class='latex inline'>y</code>, in metres, after t seconds is modelled by the equation <code class='latex inline'>y=-4t+300</code>. A second parachutist jumps <code class='latex inline'>5</code> s later and free falls for a few seconds. Her altitude, in metres, during this time, is modelled by the equation <code class='latex inline'>y = -4.9(t -5)^2 + 300</code>. When does she reach the same altitude as the first parachutist?</p>
<p>The support arches of a pedestrian bridge <strong>A</strong> can be modelled by the quadratic function <code class='latex inline'>y = -0.0044x^2 + 21.3</code> if the walkway is represented by the line <code class='latex inline'>y = 0</code>. Another bridge <strong>B</strong>, has same equation for the support arches. However, since the walkway is to be inclined slightly across a ravine, its equation is <code class='latex inline'>y = -0.0263x + 1.82</code>.</p><p><strong>a)</strong> Determine the points of intersection of the bridge support arches and the inclined walkway, to one decimal place.</p>
<p>The support arches of a pedestrian bridge <strong>A</strong> can be modelled by the quadratic function <code class='latex inline'>y = -0.0044x^2 + 21.3</code> if the walkway is represented by the line <code class='latex inline'>y = 0</code>. Another bridge <strong>B</strong>, has same equation for the support arches. However, since the walkway is to be inclined slightly across a ravine, its equation is <code class='latex inline'>y = -0.0263x + 1.82</code>.</p><p><strong>c)</strong> Determine the length of the bridge.</p>
<p>Part of the path of an asteroid is approximately parabolic and is modelled by the function <code class='latex inline'>y = -6x^2 - 370x + 100 900</code>. For the period of time that it is in the same area, a space probe is moving along a straight path on the same plane as the asteroid according to the linear equation <code class='latex inline'>y = 500x-83024</code>. A space agency needs to determine if the asteroid will be an issue for the space probe. Will the two paths intersect? Show your work.</p>
<p>The support arches of Humber River pedestrian bridge in Toronto can be modelled by the quadratic function <code class='latex inline'>y = -0.0044x^2 + 21.3</code> if the walkway is represented by the line <code class='latex inline'>y = 0</code>. A similar bridge, planned for North Bay, will have the same equation for the support arches. However, since the walkway is to be inclined slightly across a ravine, its equation is <code class='latex inline'>y = -0.0263x + 1.82</code>.</p><p>(d) How much shorter will this walkway be than the walkway that spans the Humber River in Toronto? Justify your answer.</p>
<p>A bridge has a parabolic support modelled by the equation <code class='latex inline'>\displaystyle y = -\frac{1}{200}x^2+ \frac{6}{25}x - 5</code>, where the x-axis represents the bridge surface. There are also parallel support beams below the bridge. Each support beam must have a slope of either <code class='latex inline'>0.8</code> or <code class='latex inline'>-0.8</code>. Using a slope of <code class='latex inline'>-0.8</code>, find the <code class='latex inline'>y</code>-intercept of the line associated with the longest support beam. <strong>Hint</strong>: The longest beam will be the one along the line that touches the parabolic support at just one point.</p>
How did you do?
I failed
I think I failed
I think I got it
I got it
Another question?
Found an error or missing video? We'll update it within the hour! 👉
Report it
Save videos to My Cheatsheet for later, for easy studying.