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The two positive numbers are 36 and 72 which gives a sum equal to 108 and the product of 36 and the square of 72 is a maximum.
Any integer greater than zero is considered a positive number. A positive number can either be written as a number or with the "+" symbol in front of it.
Let us consider the two positive real numbers as x and y. Then, their sum is written as,
x+y=108
Then, y=108-x
And the product is written as,
P=xy²
Substitute value of y in the above equation, we get,
Now, differentiate P with respect to x, and we get,
Solving the above equation to zero, we get,
Substitute values of x in y=108-x, to get values of y.
If we substitute x=108, we get the y value as zero which doesn't give the required solution.
But, if we substitute x=36, we get,
Thus, the two positive numbers are 36 and 72.
To know more about positive numbers:
#SPJ4
4) (a) For these problems, you should take time to familiarize yourself with common fractions that appear on the unit circle. does not appear in the unit circle unless you take the quotient 1/2 divided by sqrt(3)/2 which gives you 1/sqrt(3) which is the same as sqrt(3)/3. So our numerator is 1/2 and our denominator is sqrt(3)/2.
And remember tangent is just sin/cos. So what degree has sinx as 1/2 and and cosx as sqrt(3)/2? Well, 30 degrees does, but 30 degrees is not within the range we are given. That means they are looking for a sinx that gives us -1/2 and a cosx that gives us -sqrt(3)/2 and that is 210 degrees.
And 210 degrees in radians is 7pi/6.
I hoped that made sense.
(b) This is a lot easier. What angle gives us a cos x of -sqrt(3)/2? According to the unit circle, 150 degrees and 210 degrees does. They usually want these in radians, so the answer is 5pi/6 and 7pi/6, respectively.
5) What quadrant is radian measure 5 in?
Well 2pi or roughly 6.28 is a full circle. And 5 is slightly less than 6.28, so it is probably in quadrant IV.
But to be sure let's change 5 radian to degrees:
5 * 180/pi = 900/pi = 286.48 degrees
286.48 degrees is definitely in Q4, so we are correct.