Decompose each velocity in its i and j - coordinates.
1) River's velocity
3.5 m/s, west fo east = 3.5i + 0j
2) Luke's velocity
5m/s, 60° east of north
5* sin(60°) i + 5*cos(60°) j = 4.33 i + 2.5 j
3) Resultant velocity
[3.5i + 0j] + [4.33i + 2.5j] = 7.83i + 2.5j
resultant speed = √[ (7.83)^2 + (2.5)^2 ] = 8.22 m/s
angle = arctan(2.5 / 7.83) = 17.7° north of east (equal to 72.3° east of north).
Answer:
weeks or
weeks
Step-by-step explanation:
To do this we can set up a proportion

This will tell us how many weeks are in 2/5 of a year
Let's evaluate this
We cannot simplifiy this anymore, so we will leave it as an improper fraction, or a mixed number as shown below
weeks
Answer:
0.000036
Explanation:
When multiplying a number by 10 to the power of a positive exponent (e.g.
10
3
), move the decimal in the number that many spaces to the right (e.g.
4.5
⋅
10
3
=
4500
).
When multiplying a number by 10 to the power of a negative exponent (e.g.
10
−
4
), move the decimal in the number (the absolute value of) that many spaces to the left (e.g.
4.5
⋅
10
−
4
=
0.00045
).
For
3.6
⋅
10
−
5
, move the decimal five spaces to the left:
0.000036
Step-by-step explanation:
Answer:
Pattern: subtract 2 from the input to get the output
When the input is 9, the output is 7
When the input is 13, the output is 11
Step-by-step explanation:
» <u>Application + Solution</u>
To find the pattern, we have to look for common things we notice between the input and output.
- After analyzing, we can surely notice that we subtract two from the input each time to get the output because 3 - 2 = 1, 8 - 2 = 6, 15 - 2 = 13, and 20 - 2 = 18.
Now that we realized the pattern, we subtract 2 from 9 and 13.
Answer:
Step-by-step explanation:
<u>Slope-intercept form is:</u>
<u>Points given:</u>
<u>y-intercept is </u>
- b = 7 as per the first point
<u>And the slope is:</u>
- m = (-2 - 7)/(8 - 0) = -9/8
<u>So the line is:</u>