Respuesta :
Answer:
The maximum value of B is 45
Corrected question;
Maximize B=5xy^2, where x and y are positive numbers such that x+y^2=6.
The maximum value of B is _?
Step-by-step explanation:
Given that;
B = 5xy^2 ........1
And;
x + y^2 = 6
y^2 = 6 - x ........2
Substituting equation 2 to 1
B = 5x(6-x) = 30x - 5x^2
Maximizing B, at maximum point dB/dx = 0
dB/dx = 30 -10x = 0
30 = 10x
x = 30/10 = 3
x = 3
From equation 2;
y^2 = 6 - x = 6-3 = 3
y = √3
Maximum value of B is;
B = 5xy^2 = 5 × 3 × (√3)^2 = 45
B = 45
The maximum value of B is 45
Answer:
[tex]B = 180[/tex]
Step-by-step explanation:
The numbers are:
[tex]x = 6[/tex] and [tex]y = \sqrt{6}[/tex]
Finally, the value of B is:
[tex]B = 5\cdot (6)\cdot (6)[/tex]
[tex]B = 180[/tex]