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>
You can start by distributing the 5 to everything in the parenthesis.
5x-50=30-15x
Then get rid of your x values from one side, I chose to subtract 5x
-50 = 30 - 20x
Then subtract 30
-80=-20x
/-20
4=x
You can check by plugging your x into the equation to make sure it's right!
common difference, d = -3
f1 = -13
An arithmetic sequence f(n) = f1 + d(n - 1)
so f(n) = -13 - 3(n - 1)
f(46) = -13 - 3(46-1) = -13 -3(45) = -13 - 135 = -148
Answer:
f(46) = - 148