Answer:
b = (5±√17)/4 ≈ {0.2192, 2.2808}
Step-by-step explanation:
The average on the interval is found from the integral ...
We want the value of this integral to be 5, so we want to find b such that ...
5 = -2b^2 +5b +4
2b^2 -5b +1 = 0
b^2 -5/2b = -1/2
b^2 -5/2b +25/16 = -1/2 +25/16
(b -5/4)^2 = 17/16
b = (5±√17)/4
The average value of f(x) is 5 on the intervals ...
[0, (5-√17)/4] and [0, (5+√17)/4]
To reduce the time, the rate should be increased or the interest should be decreased
Step-by-step explanation:
the function actually is
y = 40(x - 1) + 70 = 40x - 40 + 70 = 40x + 30
still, the slope (the factor of x) is 40.
that means y (the cost) increases by 40 for every additional hour (x increases by 1).
so, the rate of change (slope) is 40/1 = $40 per hour.
Start by expanding the left hand side:
which leads to
Now we want to move all terms involving the variable to the left hand side, and all constant terms on the right hand side:
Simplify both sides by summing like terms:
Divide both sides by -8 to solve for x:
