Find the value of y...
1 answer:
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The ratio of = - 34
How to solve such questions?
Such Questions can be easily solved just by some Algebraic manipulations and simplifications. We just try to make our expression in the form which question asks us. This is the best method to solve such questions as it will definitely lead us to correct answers. One such method is completing the square method.
Completing the square is a method that is used for converting a quadratic expression of the form to the vertex form
. The most common application of completing the square is in solving a quadratic equation. This can be done by rearranging the expression obtained after completing the square:
, such that the left side is a perfect square trinomial
=
= (Completing Square method)
=
On comparing with the given equation we get
p = - and q =
∴ =
= - 34
Learn more about completing the square method here :
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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
Since 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.
