Find the value of this expression if x = 3 and y = -1. xy² 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.
I'll go out on a limb and suppose you're given the matrix
and you're asked to find the determinant of
, where
and given that
.
There are two properties of the determinant that come into play here:
(1) Whenever a single row/column is scaled by a constant
, then the determinant of the matrix is scaled by that same constant;
(2) Adding/subtracting rows does not change the value of the determinant.
Taken together, we have that
and you're asked to find the determinant of
and given that
There are two properties of the determinant that come into play here:
(1) Whenever a single row/column is scaled by a constant
(2) Adding/subtracting rows does not change the value of the determinant.
Taken together, we have that