P=10
Explanation
2p+p+90+100+140=360
3p+330=360
-330. -330
3p=30
P=10
The function is written as:
f(x) = log(-20x + 12√x)
To find the maximum value, differentiate the equation in terms of x, then equate it to zero. The solution is as follows.
The formula for differentiation would be:
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
x = (6/20)² = 9/100
Thus,
f(x) = log(-20(9/100)+ 12√(9/100)) = 0.2553
<em>The maximum value of the function is 0.2553.</em>
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Answer:

Step-by-step explanation:
As given in question, we have to find the solution of differential equation

by using the variation in parameter method.
From the above equation, the characteristics equation can be given by



Since, the roots of characteristics equation are real and distinct, so the complementary function of the differential equation can be by

Let's assume that


and g(t)=1
Now, the Wronskian can be given by




Now, the particular solution can be given by





Now, the complete solution of the given differential equation can be given by

