How many whole weeks are in a year
1 answer:
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Option A: is the dilation factor
Explanation:
The Coordinates of the square ABCD are A(-21,18), B(-12,18), C(-12,9), D(-21,9)
Also, the coordinates of the square A'B'C'D' are A'(–7, 6), B'(-4,6), C'(-4,3), D'(-8,3)
Now, we shall determine the scale factor in the dilation if the coordinates A' and C'.
Since, the dilation is the enlargement of the image in the same shape but different size.
To determine the scale factor, let us divide A'C' by AC
Thus, we have,
Also,
Dividing A'C' by AC, we have,
Thus, is the dilation factor
Answer:
1) Volume occupied by the spheres are equal therefore the three tanks contains the same volume of water
2)
Step-by-step explanation:
1) Here we have;
First tank A
Volume of tank = x³
The volume of the sphere =
However, the diameter of the sphere = x therefore;
r = x/2 and the volume of the sphere is thus;
volume of the sphere = =
For tank B
Volume of tank = x³
The volume of the spheres =
However, the diameter of the spheres 2·D = x therefore;
r = x/4 and the volume of the sphere is thus;
volume of the spheres =
For tank C
Volume of tank = x³
The volume of the spheres =
However, the diameter of the spheres 4·D = x therefore;
r = x/8 and the volume of the sphere is thus;
volume of the spheres =
Volume occupied by the spheres are equal therefore the three tanks contains the same volume of water
2) For the 4th tank, we have;
number of spheres on side of the tank, n is given thus;
n³ = 512
∴ n = ∛512 = 8
Hence we have;
Volume of tank = x³
The volume of the spheres =
However, the diameter of the spheres 8·D = x therefore;
r = x/16 and the volume of the sphere is thus;
volume of the spheres =
Amount of water remaining in the tank is given by the following expression;
Amount of water remaining in the tank = Volume of tank - volume of spheres
Amount of water remaining in the tank =
.