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: A. A(1) = 14; A(n) = (n − 1) −4; A(n) = 14 + (n − 1)(−4)
Step-by-step explanation:
Arithmetic sequence is a sequence that is identified by their common difference. Let a be the first term, n be the number of terms and d be the common difference.
For an arithmetic sequence, common difference 'd' is added to the preceding term to get its succeeding term. For example if a is the first term of a sequence, second term will be a+d, third term will give a+d+d and so on to generate sequence of the form,
a, a+d, a+3d, a+4d...
Notice that each new term keep increasing by a common difference 'd'
The nth term of the sequence Tn will therefore give Tn = a+(n-1)d
If the initial (first) term is 14 and common difference is -4, the nth of the sequence will be gotten by substituting a = 14 and d = -4 in the general formula to give;
Tn = 14+(n-1)-4 (which gives the required answer)
Tn = 14-4n+4
Tn = 18-4n
Answer:
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Step-by-step explanation:
The sum of a straight angle is 180°
So 77+x=180
Subtract 77 from both sides and the equation is
x=77
The measure of the other angle is 77°
The line x = 0 is perpendicular to the line y = -3:
Correct. Any horizontal line (y = a) and any vertical line (x = b) intersect at some point and are perpendicular.
All lines that are parallel to the y-axis are vertical lines:
Correct. The y-axis is a vertical line, so any lines that are parallel to it must also be vertical.
All lines that are perpendicular to the x-axis have a slope of 0.
Incorrect. Lines that have a slope of 0 are horizontal, and the x-axis is horizontal as well. Any lines with a slope of 0 are <em>parallel </em>to the x-axis, not perpendicular to it.
The equation of the line parallel to the x-axis that passes through the point (2, 6) is x = 2.
Incorrect. x = 2 is a vertical line, and vertical lines cannot be parallel to the horizontal x-axis. x = 2 is perpendicular to the x-axis, however.
The equation of the line perpendicular to the y-axis that passes through the point (-5, 1) is y = 1.
Correct. The line y = 1 is horizontal, and the y-axis is a vertical line. Because the line y = 1 crosses the y-axis, the lines are perpendicular.
