Find two positive numbers that satisfy the given requirements. The sum of the first number squared and the second number is 54 and the product is a maximum.

36

Step-by-step explanation:

Calculation to Find two positive numbers

First step

Let the first positive number be a

Let the second positive number be b

Second step is to create the Equation

a^2+b= 54 Equation (1)

b = 54-a^2 Equation (2)

Third step is to find the product

Product= a(54-a)^2 = 54a-a^3

Fourth step is to differentiate

dP/dx = 54-3a^2

dP/dx = 0

Fifth step is to solve for 54-3a^2 = 0

Hence,

3a^2=54

a^2 = 18

Last step

a= √(18)

b= 54-(√(18))^2

b=54-18

b = 36

Therefore the two positive numbers are 36

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.  

these sign is used to tell weather the number is greater or less than the number   <   or >     but this sign means its equal =    

hope this you and

step-by-step explanation: