Answer:
Let the total distance Aileen ran be 'x'
Let the distance ran by Andrew be 'y'
Refer to graph attached for graphical representation of distance travelled by both.
Applying the formula,
distance=speed*time
x=20*t Equation 1
y= 15*t equation 2
Since it can be easily understood by the graph attached, that
x=150+y equation 3
Now putting values of x and y in equation 3
20*t =150 +15*t.
5t= 150
t=30 seconds.
putting the values of t in both the equation 1 and 2
x=20t
=20*30
x = 600 feet
So the distance ran by Aileen is 600 feet, whereas Andrew ran 450 feet.
Step-by-step explanation:
Do not mind the names just change them. I had the same question before with different names so that is why. Hope this helps:)
Answer:
The rectangular coordinates of the point are (3/2 , √3/2)
Step-by-step explanation:
* Lets study how to change from polar form to rectangular coordinates
- To convert from polar form (r , Ф) to rectangular coordinates (x , y)
use these rules
# x = r cos Ф
# y = r sin Ф
* Now lets solve the problem
∵ The point in the rectangular coordinates is (√3 , π/6)
∴ r = √3 and Ф = π/6
- Lets find the x-coordinates
∵ x = r cos Ф
∵ r = √3
∵ Ф = π/6
∴ x = √3 cos π/6
∵ cos π/6 = √3/2
∴ x = √3 (√3/2) = 3/2
* The x-coordinate of the point is 3/2
- Lets find the y-coordinates
∵ y = r sin Ф
∵ r = √3
∵ Ф = π/6
∴ y = √3 sin π/6
∵ sin π/6 = 1/2
∴ y = √3 (1/2) = √3/2
* The y-coordinate of the point is √3/2
∴ The rectangular coordinates of the point are (3/2 , √3/2)
Answer:
5
Step-by-step explanation:
you would do 42 divided by 7 which is 6 then subtract 2 from 7 and you would get 5
Answer:
It is an arithmetic sequence and the common difference is 5
Step-by-step explanation:
4+5 = 9; 9+5=14 (adding is arithmetic, multiplying is geometric)
Substitute the first equation into the second equation. You will get:
4x - (2x - 5) = 7
Distribute the negative sign into the parenthesis:
4x - 2x + 5 = 7
Simplify
2x + 5 = 7
Subtract 5 on both sides
2x = 2
x = 1
Now, substitute x = 1 into the first equation:
y = 2(1) - 5
y = 2 - 5
y = -3
The solution to the system of equations is (1, -3).
