Given:
The function that represents how the amount of fuel changes as a function of distance flown is
where x represents miles flown, and f(x) represents the amount of fuel remaining.
To find:
The rate of change for this scenario.
Solution:
The slope intercept form of a linear function is
...(i)
Where, m is the slope or rate of change and b is the y-intercept.
We have,
...(ii)
On comparing (i) and (ii), we get
Therefore, the rate of change for this scenario is -0.9. It means, the amount of fuel in the airplane is decreasing by 0.9 gallons per mile.
Answer:
698 fishes
Step-by-step explanation:
Generally, we can represent an exponential growth function as;
y = a•(1 + r)^t
originally, there were 3 fishes
The original value in this case means a = 3
After 6 weeks, there were 31
31 in this case is y
r is the increase percentage or rate
t is the time
So, we have it that;
31 = 3•(1 + r)^6
31/3 = (1 + r)^6
10.33 = (1 + r)^6
ln 10.33 = 6 ln (1 + r)
ln 10.33/6 = ln (1 + r)
e^0.3892 = (1 + r)
1 + r = 1.476
r = 1.476-1
r = 0.476 or 47.6%
So the growth percentage or rate is 47.6%
For 14 weeks, we simply have the value of t as 14;
So ;
y = 3•(1 + 0.476)^14
y = 3(1.476)^14
y = 698 fishes
IF IT EQUALS 0
1. find two number that multiplied to 48 and adds to 14, which are 6 and 8.
2. substitute the new numbers in with x to get x^2 + 6x + 8x + 48.
3. factor out the x and the 8 to get x(x+6)+8(x+6).
4. x = -6, x = -8
IF IT DOES NOT EQUAL 0
then (x+6)*(x+8) is your answer.
One-thousand five-hundred and sixty divided by twenty four is sixty five
Answer:
There were 261 Cheeseburgers and 87 Hamburgers sold on Tuesday
Step-by-step explanation:
Lets write some equations where H=Hamburgers and C=Cheeseburgers:
1) H+C=348
2) C=3H
1) Substitute 3H as C in the first equation:
3H+H=348
2) Combine alike terms:
4H=348
3) Divide both sides by 4:
H=87
4) Now, substitute 87 as H in the first equation:
87+C=348
5) Subtract 87 from both sides:
C=261
