A) 4a - 3b + 2c
4(2, -1, 5) - 3(4, 3 , -2) + 2(5, 4, 0) = (8, -4, 20) - (12, 9, - 6) + (10, 8, 0) =
= (8 - 12 + 10 , -4 - 9 + 8 , 20 + 6 + 0) = (6, - 5, 26)
Answer: (6, - 5, 26)
b) magnitude of vector b

c) vector of length 7 parallel to vector c
=> m(5,4,0) = (5m,4m,0)
=>

=> m = 7 / √41 ≈ 1.093
=> 1.093 (5, 4, 0) = (5.465 , 4.372, 0)
Answer: (5.465 , 4.372 , 0)
Answer:
the area of grass is 314 square feet
Step-by-step explanation:
The radius of the circle the goat can reach is given by the length of the rope that ties the goat to the post (10 ft)
Then the area of the circle is: 
So the area of grass is 314 square feet
<h2>Plastic Beads = $0.50</h2><h2>Metal Beads = $0.75</h2><h2 />
p = Plastic Beads
m = Metal Beads
Equations:
7p + 5m = 7.25
9p + 3m = 6.75
Make one pair of coefficients the same:
3 * (7p + 5m = 7.25) = 21p + 15m = 21.75
5 * (9p + 3m = 6.75) = 45p + 15m = 33.75
Remove that coefficient;
(45p + 15m) - (21p + 15m) = 33.75 - 21.75
(45p - 21p ) + ( 15m - 15m) = 33.75 - 21.75
24p = 12
24p / 24 = 12 / 24
<h3><u>p = 0.5</u></h3><h3 />
Substitute the result into one of the original equations.
(7 * 0.5) + 5m = 7.25
Rearrange to find the missing value:
7.25 - (7 * 0.5) = 5m
7.25 - 3.5 = 3.75
5m = 3.75
5m / 5 = 3.75 / 5
<h3><u>m = 0.75</u></h3>