Answer:
Step-by-step breakdown:
The necessary formula for this problem is
which resolves to
leading to
36 + 6x = 40 + 5x, and consequently
x = 4
Thus, DG equals 5 + 4 + 3, resulting in 12
The function can be expressed as:
f(x) = log(-20x + 12√x)
To ascertain the maximum value, differentiate the equation with respect to x and set the derivative to zero. The procedure unfolds as follows.
The differentiation formula is:
d(log u)/dx = du/u ln(10)
Thus,
d/dx = (-20 + 6/√x)/(-20x + 12√x)(ln 10) = 0
-20 + 6/√x = 0
6/√x = 20
From which we derive x = (6/20)² = 9/100
Therefore,
f(x) = log(-20(9/100)+ 12√(9/100)) = 0.2553
The function's maximum value is 0.2553.
Answer:
The height is 11.76 meters.
Step-by-step explanation:
To solve this problem, the following equations are necessary:
The first one relates initial and final velocities, taking into account that gravity is 9.81 m/s² and the time is 0.3 seconds:
Vf = Vo + g * t = Vo + 9.81 * 0.3
Vf = Vo + 2.94 (1)
The second one also connects initial and final velocities, but this time with distance S, which we know to be 5 meters:
Vf² = Vo² + 2 * g * S
Vf² = Vo² + 2 * 9.81 * 5
Vf² = Vo² + 98.1 (2)
We now have two equations with two unknowns. By substituting (1) into (2):
(Vo + 2.943)² = Vo² + 98.1
Vo² + 5.886 * Vo + 8.66 = Vo² + 98.1
Canceling Vo² and rearranging gives us:
Vo = 89.44 / 5.886
Vo = 15.195 m/s
Now using the formula:
Vo² = 2 * g * h
h = Vo² / (2 * g) = (15.195²) / (2 * 9.81) = 11.76 meters
So, the height corresponds to 11.76 meters.
