What is The equation of a vertical line passing through the point (-5,-1)
2 answers:
Answer:
The answer is x=-5
Step-by-step explanation:
In order to determine the equation, we need to know about vertical line equations.
In general, a line equation has the form:
Where "y" is the dependent variable, "x" is the independent variable, "m" is the slope of the line and "n" is the value where the line cuts the "y" axis.
A vertical line, x only takes one value. Thus, the equation for a vertical line is x = a, where a is the value that x takes.
So for the coordinate (-5,-1), the vertical line has to pass through the "x" value, that it is -5, therefore the equation of a vertical line passing through the point (-5,-1) is:
x=-5
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Given:
The width at the base of parabolic tunnel is 7 m.
The ceiling 3 m from each end of the base there are light fixtures.
The height to light fixtures is 4 m.
To find:
Whether it is possible a trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel.
Solution:
The width at the base of tunnel is 7 m.
Let the graph of the parabola intersect the x-axis at x=0 and x=7. It means x and (x-7) are the factors of the height function.
The function of height is:
...(i)
Where, a is a constant.
The ceiling 3 m from each end of the base there are light fixtures and the height to light fixtures is 4 m. It means the graph of height function passes through the point (3,4).
Putting x=3 and h(x)=4 in (i), we get
Putting , we get
...(ii)
The center of the parabola is the midpoint of 0 and 7, i.e., 3.
The width of the truck is 4 m. If is passes through the center then the truck must m 2 m on the left side of the center and 2 m on the right side of the center.
2 m on the left side of the center is x=1.5.
A trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is possible if h(1.5) is greater than 2.8.
Putting x=1.5 in (ii), we get
It is clear that h(1.5)<2.8, therefore the trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is not possible.
