Answer and Step-by-step explanation:
Let x and y be two positive integers and their sum is 14:
X + y = 14
And the sum of square of this number is:
f = x2 + y2
= x2+ (14 – x)2
Differentiate with respect to x, we get:
F’(x) = [ x2 + (14 – x)2]’ = 0
2x + 2(14-x)(-1) = 0
2x +( 28 – 2x)(-1) = 0
2x – 28 +2x = 0
2x + 2x = 28
4x = 28
X = 7
Hence, y = 14 – x = 14 -7 = 7
Now taking second derivative test:
F”(x) > 0
For x = y = 7,f reaches its maximum value:
(7)2 + (7)2 = 49 + 49
= 98
F at endpoints x Є [ 0, 14]
F(0) = 02 + (14 – 0)2
= 196
F(14) = (14)2 + (14 – 14)2
= 196
Hence the sum of squares of these numbers is minimum when x = y = 7
And maximum when numbers are 0 and 14.
Answer:
The length of the second side is 22.5 feet.
Step-by-step explanation:
Answer:
8.3
Step-by-step explanation:
25÷3=8.3333333
I rounded it to this.
b=3
I found this out by subtracting and adding on both sides.
Let d represent number of days and n represent number of workers.
We have been given that when building a house, the number of days required to build varies inversely with with the number of workers.
We know that the equation 
represents the relation where y is inversely proportional to x and k is the constant of proportionality.
So our required equation would be 
Upon substituting our given values, we will get:
Since constant of proportionality is 665, so our equation would be 
.
To find the number of days it will take to build a similar house with 5 workers, we will substitute 
in our equation as:
Therefore, it will take 133 days for 5 workers to build a similar house.
