You multiply vectors and scalar simply by multiplying each component by that scalar:

Finally, you sum two vectors by summing the correspondent coordinates:

To complete the square you need to halve the linear coefficient -4/2, square it, 4, and add that value, giving you:
x^2-4x+4 and that is a perfect square equal to:
(x-2)^2
Answer:
15 figures
Step-by-step explanation:
To know with this, and knowing that each dimension is 10% longer, let's do a simple example assuming some random values.
Let's suppose that you have cylinder with a radius of 3 cm and height of 5 cm. The volume of this cylinder is:
V = π*(3)^2*5 = 45π cm^3
Now, if we raise the dimensions by 10%, the radius and height will be 3.3 and 5.5 respectively so, the new volume (V2) will be:
V2 = π*(3.3)^2*5.5 = 59.9π cm^3
So the ratio of both volumes is:
59.9π/45π = 1.331
This means that each new solid would have 1.331 times the volume of the original solid. Therefore, we can stablish a relation between the original figures and the new ones calling "x" the number of new figures so:
20 = 1.331x
solving for x:
x = 20/1.331
x = 15.03
You can round this to 15.
Answer:
The volume of the softball is 6.6 times the volume of the tennis ball
Step-by-step explanation:
we know that
The volume of a sphere is equal to

step 1
Find the volume of the softball
we have

substitute

step 2
Find the volume of the tennis ball
we have

substitute

step 3
Divide the volume of the softball by the volume of the tennis ball

therefore
The volume of the softball is 6.6 times the volume of the tennis ball
<em>Alternative Method</em>
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
The scale factor is equal to the ratio of its radius

therefore
The scale factor elevated to the cube is

therefore
The volume of the softball is 6.6 times the volume of the tennis ball
A hex key maybe? (: if you have any other question feel free to send me a link