Apex Grocery wants to build a warehouse that is exactly five miles from each of the routes between stores L, M, and N. Which con
struction correctly finds the best location of the warehouse?
1 answer:
Answer: Option C - Construction Y because point E is the circumcentre of triangle LMN.
Point E is the best location for the warehouse as it is exactly equidistant from the three stores at L, M and N.
Step-by-step explanation:
Before solving an algebra problem, it sometimes helps to get a geometric picture of what's happening. Geometry says that three points determine a circle - in other words, given three points that are not
all on the same line, there is exactly one circle which passes through all 3. Finding the point equidistant from the 3 points is the same thing as finding the center of the circle that passes through all of them (since all points on a circle are equidistant from the center).
Our points are L, M and N. Draw the lines LM, LN and MN to form a triangle. Now construct the perpendicular bisectors of any two of the lines, and their intersection, point E, will be the center of this circle.
As shown in the Construction Y because E is the circumcentre of triangle LMN.
This is the best location for the warehouse as it is exactly equidistant from the three stores at L, M and N.
QED!
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Answer:
The rocket will take 4.5 seconds to reach its maximum height.
Step-by-step explanation:
The height of a missile t seconds after it has been fired is given by h=-4.9*t²+44.1*t
This function is a quadratic function of the form f (x) = a*x² + b*x + c. In this case a=-4.9, b=44.1 and c=0
To calculate how many seconds it will take for the rocket to reach its maximum height, I must calculate the maximum of the function. The maximum of a quadratic function is the vertex of the parabola. The x coordinate of the vertex will be simply: . The y coordinate of the vertex corresponds to the function evaluated at that point.
In this case the x coordinate of the vertex corresponds to the t coordinate. In other words, by calculating the x coordinate of the vertex, you are calculating the maximum time t it will take for the rocket to reach its maximum height. So:
t=4.5
<u><em>The rocket will take 4.5 seconds to reach its maximum height.</em></u>