Answer:
h = 1,743
Step-by-step explanation:
Volume of a box is
V(h) = ( A - 2h) * ( B - 2h)* h A = 7 B = 12
We have
V(h) = ( 7 - 2h) * ( 12 - 2h ) * h
V(h) = ( 84 - 14*h - 24*h + 4*h² ) * h
V(h) = ( 84 - 38*h + 4 *h² ) * h ⇒ V(h) = 84h - 38h² + 4h³
Taking derivatives both sides of the equation
V´(h) = 84 - 76h + 12x²
V´(h) = 0 84 - 76h + 12x² = 0 42 - 38h + 6x²
3x² - 19h + 24 = 0
Solving for h h1 = [ ( 19 + √(19)² - 288 ]/ 6 h1 = [ (19 + √73)/6]
h₁ = 4,59 we dismiss this value since 9,18 (4,59*2) > A
h₂ = [ 19 - √73)/6] h₂ = 1,743
h = 1.743 is h value to maximizes V
Answer:
I think the y intercept would be 2.125 (round as needed)
Step-by-step explanation:
If on x2 the y is 8.5, divide that by 2 to get x1. So (1,4.25) now. Then divide by 2 again to get (0,2.125)
I could be wrong, but I hope I'm right haha
Answer:
the solution to the equations is :-
(4,3)
Step-by-step explanation:
here's the solution :-
=》x + 2y = 10
=》x = 10 - 2y
now, plugging the value of x in other equation :-
=》9x - 2y = 30
=》9 × (10 - 2y) - 2y = 30
=》90 - 18y -2y = 30
=》-20y = 30 - 90
=》y = -60 ÷ -20
=》y = 3
now, plugging the value of y in first equation,
=》x = 10 - 2y
=》x = 10 - (2×3)
=》x = 10 - 6
=》x = 4
so, the solution of the system is (4,3)
