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>
Hello :
f(x) = <span>a(x-k)²+k....... the point vertex is (h , k )
in this exercice : h = -3 and k = -1 s0 f(x) = a(x+3)²-1
find : a
but f(0)=8
a(0+3)² -1 = 8
9a-1=8
9a =9
a=1
f(x) =(x+3)²-1 =x²+6x+9-1
f(x) = x²+6x+8 .... (</span><span>the quadratic function in standard form )</span>
Answer:

Step-by-step explanation:

Answer:
15
Step-by-step explanation:
let r represent red marbles then white = 2r + 5 and total is 20, thus
r + 2r + 5 = 20 ( subtract 5 from both sides )
3r = 15 ( divide both sides by 3 )
r = 5 ← number of red marbles
Thus number of white = 20 - 5 = 15