3 gallons x 4 qt/gallon = 12 quarts total.
He used 9, so he has 12 qt. - 9 qt. remaining.
3 Quarts remain.
Answer:
b = 3/8
Step-by-step explanation:
Solve for b:
b + 1/8 = 1/2
Put each term in b + 1/8 over the common denominator 8: b + 1/8 = (8 b)/8 + 1/8:
(8 b)/8 + 1/8 = 1/2
(8 b)/8 + 1/8 = (8 b + 1)/8:
(8 b + 1)/8 = 1/2
Multiply both sides of (8 b + 1)/8 = 1/2 by 8:
(8 (8 b + 1))/8 = 4
(8 (8 b + 1))/8 = 8/8×(8 b + 1) = 8 b + 1:
8 b + 1 = 4
8/2 = (2×4)/2 = 4:
8 b + 1 = 4
Subtract 1 from both sides:
8 b + (1 - 1) = 4 - 1
1 - 1 = 0:
8 b = 4 - 1
4 - 1 = 3:
8 b = 3
Divide both sides of 8 b = 3 by 8:
(8 b)/8 = 3/8
8/8 = 1:
Answer: b = 3/8
Answer:
- -108.26
- -108.13
- -108.052
- -108.026
- -108
Step-by-step explanation:
A graphing calculator or spreadsheet is useful for making the repeated function evaluations required.
The average velocity on the interval [a,b] will be ...
v avg = (y(b) - y(a))/(b-a)
Here, all the intervals start at a=3, so the average velocity for the given values of t will be ...
v avg = (y(3+t) -y(3))/((3+t) -3) = (y(3+t) -y(3))/t
This can be computed for each of the t-values given. The results are shown in the attached table.
__
We note that the fractional part of the velocity gets smaller in proportion to t getting smaller. We expect it to go to 0 when t goes to 0.
The estimated instantaneous velocity is -108 ft/s.
_____
We can simplify the average velocity equation to ...
v avg = ((48(3+t) -26(t+3)^2) -(48(t+3) -26(3)^2)) / t
= (48t -26(t^2 +6t))/t
= 48 -26t -156
<em> v avg = -108 -26t</em>
Then the average velocity at t=0 is -108.