Answer: 12 hours
Step-by-step explanation:
Let x = time it takes to fill the pool if the inlet pipe and drain pipe are both open
1/6 = portion of pool filled per hour by the inlet pipe
1/12 = portion of pool emptied per hour by the drain
1/x = portion of pool filled per hour if the inlet pipe and drain are both open
Then, 1/6 - 1/12 = 1/x
Multiply by the LCD, 12x, to obtain
2x - x = 12
x = 12 hours
Steps:
1) determine the domain
2) determine the extreme limits of the function
3) determine critical points (where the derivative is zero)
4) determine the intercepts with the axis
5) do a table
6) put the data on a system of coordinates
7) graph: join the points with the best smooth curve
Solution:
1) domain
The logarithmic function is defined for positive real numbers, then you need to state x - 3 > 0
=> x > 3 <-------- domain
2) extreme limits of the function
Limit log (x - 3) when x → ∞ = ∞
Limit log (x - 3) when x → 3+ = - ∞ => the line x = 3 is a vertical asymptote
3) critical points
dy / dx = 0 => 1 / x - 3 which is never true, so there are not critical points (not relative maxima or minima)
4) determine the intercepts with the axis
x-intercept: y = 0 => log (x - 3) = 0 => x - 3 = 1 => x = 4
y-intercept: The function never intercepts the y-axis because x cannot not be 0.
5) do a table
x y = log (x - 3)
limit x → 3+ - ∞
3.000000001 log (3.000000001 -3) = -9
3.0001 log (3.0001 - 3) = - 4
3.1 log (3.1 - 3) = - 1
4 log (4 - 3) = 0
13 log (13 - 3) = 1
103 log (103 - 3) = 10
lim x → ∞ ∞
Now, with all that information you can graph the function: put the data on the coordinate system and join the points with a smooth curve.
Answer: Nick must now at least 6 yards.
Step-by-step explanation:
Since Nick has $80 saved already, and he makes $40 per yard that he mows, thus can be put up in an equation as:
= 80 + 40y
where y = number of yards
Since Nick needs to raise at least $320 for his trip, the equation to solve this will be:
80 + 40x ≥ 320
40x ≥ 320 - 80
40x ≥ 240
x ≥ 240/40
x ≥ 6
Therefore, Nick must now at least 6 yards.
Answer:
4n+2
Step-by-step explanation:
- add all sides =9n+3
- 3n+2+2n-1=9n+3
- add liketerms 5n+1=9n+3
- put liketerms together 9n-5n+3-1
- ans hence is 4n+2
Answer:
8
Step-by-step explanation:
The domain is from the points (-4,0) through (4,0).
