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>
Answer:
54.2 mph
Step-by-step explanation:
Since the drivers leave at the same time and travel in directions 90° from each other, their separation speed can be found using the Pythagorean theorem. Let c represent Cynthia's average speed. Then (c-10) will represent Tim's average speed. Their combined separation speed is 70 miles per hour, so we can write ...
70² = c² +(c -10)²
4900 = 2c² -20c +100 . . . . eliminate parentheses
c² -10c -2400 = 0 . . . . . . . . divide by 2; put in standard form
(c -5)² -2425 = 0 . . . . . . . . . rearrange to vertex form
c = 5 ±5√97 . . . . . . . . . . . . solve for c, simplify radical
c ≈ 54.244 ≈ 54.2 . . . . . . . use the positive solution
Cynthia's average speed was 54.2 miles per hour.
Answer: 2592
Step-by-step explanation:
Product means to multiple.
Since product means to multiple, we multiple 54 x 48 to get 2592
