What is the domain of this function. (Could someone explain it too? I wanna be able to do it myself as well)
1 answer:
You might be interested in
Answer: vector equation r = (7+3t)i + (4+2t)j + (5 - 5t)k
parametric equations: x = 7 + 3t; y = 4 + 2t; z = 5 - 5t
Step-by-step explanation: The vector equation is a line of the form:
r = + t.v
where
is the position vector;
v is the vector;
For point (7,4,5):
= 7i + 4j + 5k
Then, the equation is:
r = 7i + 4j + 5k + t(3i + 2j - k)
<u><em>r = (7 + 3t)</em></u><u><em>i</em></u><u><em> + (4 + 2t)</em></u><u><em>j </em></u><u><em>+ (5 - 5t)</em></u><u><em>k</em></u>
The parametric equations of the line are of the form:
x = + at
y = + bt
z = + ct
So, the parametric equations are:
<em><u>x = 7 + 3t</u></em>
<em><u>y = 4 + 2t</u></em>
<em><u>z = 5 - 5t</u></em>
The best description of the resulting three-dimensional figure when the considered figure is revolved is: A cylinder with height 24 cm.
<h3>What is solid of revolution?</h3>When a figure is revolved around some fixed axis, the whole three dimensional solid formed from the area that it swaps out is called solid of revolution.
Since no image is specified, we will work on the image attached below.
We can visualize and imagine that the horizontal line is still and just rotating on its place. The rectangle will revolve around, and therefore will swap out a cylindrical shape.
Since the length of the rectangle is 24 cm, and it is rotated on its length, so that will serve as height of the formed cylinder.
Thus, the best description of the resulting three-dimensional figure when the considered figure is revolved is: A cylinder with height 24 cm.
Learn more about solid of revolution here:
