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>
Answer: 0.9013
Step-by-step explanation:
Given mean, u = 10, standard deviation =8
P(X) =P(Z= X - u /S)
We are to find P(X> or =12)
P(X> or = 12) = P(Z> 12-10/8)
P(Z>=2/8) = P(Z >=0.25)
P(Z) = 1 - P(Z<= 0.25)
We read off Z= 0.25 from the normal distribution table
P(Z) = 1 - 0.0987 = 0.9013
Therefore P(X> or=12) = 0.9013
Note the question was given as an incomplete question the correct and complete question had to be searched online via Google. So the data used are those gotten from the online the Googled question.
Answer:
The value of k is 3.
Step-by-step explanation:
The function f(x) passes through the points (0,4) and (-6,-2)
So the equation of the function is 
⇒ y = x + 4 ....... (1)
Again the function g(x) passes through the points (0,4) and (-2,-2).
Therefore, the equation of g(x) will be 
⇒ y = 3x + 4
Therefore, g(x) = 3x + 4 = f(3x) {from equation (1).
So, the value of k is 3. (Answer)
Answer:
16 years
Step-by-step explanation:
Let x represent the number of years. The suburb population is growing at a rate of 5000 per year after x years, it can be represented by the equation:
320000 + 5000x
The city population is declining at a rate of 14000 per year after x years, it can be represented by the equation:
624000 - 14000x
The number of years for the city and suburb population to be equal can be gotten from:
320000 + 5000x = 624000 - 14000x
14000x + 5000x = 624000 - 320000
19000x = 304000
x = 304000 / 19000
x = 16
In 16 years the populations of the suburb and the city be equal
Answer:
28
Step-by-step explanation:
We have the following function:
where a=-3, b=168 and c=-1920
In order to calculate the maxium profit for the company, and how many cakes should be prepared in order to reach it, we have to calculate where the parabola's vertex is ubicated. To do so, we use the following formula:
So 28 cakes should be prepared per day in order to maximize profit.
