Part I)
The module of vector AB is given by:
lABl = root ((- 3) ^ 2 + (4) ^ 2)
lABl = root (9 + 16)
lABl = root (25)
lABl = 5
Part (ii)
The module of the EF vector is given by:
lEFl = root ((5) ^ 2 + (e) ^ 2)
We have to:
lEFl = 3lABl
Thus:
root ((5) ^ 2 + (e) ^ 2) = 3 * (5)
root ((5) ^ 2 + (e) ^ 2) = 15
Clearing e have:
(5) ^ 2 + (e) ^ 2 = 15 ^ 2
(e) ^ 2 = 15 ^ 2 - 5 ^ 2
e = root (200)
e = root (2 * 100)
e = 10 * root (2)
It is
hypotenuses^2 = base^2 + perpendicular^2
hope it helped
-9 is a rattional number because it is an integer and it can be squared.
The first step to solve this problem is to compute first for
the area of the bigger rectangle:
A = LW
A = 12m (10m)
A = 120 m^2
Next step is to find the area of the smaller rectangle:
A = LW
A = 7m (2m)
A = 14 m^2
The last step is to deduct the area of the smaller rectangle
to the area of the larger rectangle:
Area of larger rectangle – Area of the smaller rectangle =
Area of the shaded region
120 m^2 – 14 m^2 = 106 m^2
Therefore, the area of the shaded region is 106 square
meters.
