Answer:
The vector that describes their hike from their starting position to their final destination is ![\vec r = 7\,\hat{i}+1\,\hat{j}\,\,\,[mi]](https://tex.z-dn.net/?f=%5Cvec%20r%20%3D%207%5C%2C%5Chat%7Bi%7D%2B1%5C%2C%5Chat%7Bj%7D%5C%2C%5C%2C%5C%2C%5Bmi%5D)
.
Step-by-step explanation:
In this problem we assume that orthogonal axes coincide with the north and east. We proceed to translate each sentence from statement into vectorial equations:
(i) <em>A group of hikers walks 3 miles east and then 1 mile north:</em>
![\vec r_{A} = 3\,\hat{i}+1\,\hat{j}\,\,\,[mi]](https://tex.z-dn.net/?f=%5Cvec%20r_%7BA%7D%20%3D%203%5C%2C%5Chat%7Bi%7D%2B1%5C%2C%5Chat%7Bj%7D%5C%2C%5C%2C%5C%2C%5Bmi%5D)
(ii) <em>After taking a break, they then hike 4 miles east to their final destination:</em>
![\vec r_{B} = 4\,\hat{i}\,\,\,[mi]](https://tex.z-dn.net/?f=%5Cvec%20r_%7BB%7D%20%3D%204%5C%2C%5Chat%7Bi%7D%5C%2C%5C%2C%5C%2C%5Bmi%5D)
The vector that describes their hike from their starting position to their final destination is the sum of the vectors deducted above. That is:
(1)
![\vec r = (3\,\hat{i}+1\,\hat{j})+4\,\hat{i}\,\,\,[mi]](https://tex.z-dn.net/?f=%5Cvec%20r%20%3D%20%283%5C%2C%5Chat%7Bi%7D%2B1%5C%2C%5Chat%7Bj%7D%29%2B4%5C%2C%5Chat%7Bi%7D%5C%2C%5C%2C%5C%2C%5Bmi%5D)
The vector that describes their hike from their starting position to their final destination is .
Answer:
Step-by-step explanation:
<u>1) Find the radius</u>
We can do this by using the distance equation with the centre (7,1) and the given point (-1,-5):
where the two points are 
and 
Plug in the points (7,1) and (-1,-5)
Therefore, the radius of the circle is 10 units.
<u>2) Plug the data into the equation of a circle</u>
Equation of a circle (when not centred at the origin):
where the centre is 
and r is the radius
Plug in the centre (7,1) as (h,k)
Plug in the radius 10
I hope this helps!
The answer to that problem is 800
Answer:
138
Step-by-step explanation:
Add the amount of garbage that Ralph and Kyle threw out to get the answer;
72 + 66 = 138
Answer:
b=2A/h-a
Step-by-step explanation:
A=1/2h(a+b)
Multiplying by 2
2A=h(a+b)
Dividing by h
2A/h=a+b
Subtracting a
2A/h-a =b
b=2A/h-a
