The local hardware store has blue buckets that hold 2 gallons of water and white buckets that hold 5 gallons of water. You bought 7 buckets that can hold 26 gallons of water. How many buckets of each color were purchased?

3 blue buckets and 4 white buckets were purchased.

Step-by-step explanation:

Let x represent the number of blue buckets that were purchased.

Let y represent the number of white buckets that were purchased.

The local hardware store has blue buckets that hold 2 gallons of water and white buckets that hold 5 gallons of water. The buckets that you bought can hold 26 gallons of water. This means that

2x + 5y = 26 - - - - - - - - - - - - -1

The number of buckets that you bought is 7. This means that

x + y = 7

Substituting x = 7 - y into equation 1, it becomes

2(7 - y) + 5y = 26

14 - 2y + 5y = 26

- 2y + 5y = 26 - 14

3y = 12

y = 12/3

y = 4

x = 7 - y = 7 - 4

x = 3

at s = 10m, v(t_1) =  7.663 m/s

at s = 15m, v(t_2) = 10.041 m/s

Step-by-step explanation:

for the interval 0-10 seconds,

a(t) = t m/s^2

v(0) = 0

v(t) = v(0) + integral(a(t)dt)

= 0 +  [t^2/2]  

= (1/2) t^2

s(0) = 0       arbitrary

s(t) = s(0) + integral(v(t)dt)

= 0 + integral ((1/2)t^2)

= (1/6)t^3

When s(t) = 10 m,

(1/6)t^3 = 10

t^3 = 60

t_1 = 60 ^(1/3) = 3.9149 s approx.

v(t_1) = (1/2) t_1^2 = (1/2)3.9149^2 = 7.663 m/s

When s = 15 m

(1/6)t^3 = 15

t^3 = 90

t_2 = 4.4814 s approx.

v(t_2) = (1/2)t_2^2 = (1/2)4.4814^2 = 10.041 m/s