SA=2H(L+W)+LW for open box
20=2H(4+W)+4(W)
distribute
20=8H+2WH+4W
divide both sides by 2
10=4H+WH+2W
solve for 1 variable, pick W
10-4H=WH+2W
10-4H=W(H+2)
(10-4H)/(H+2)=W
V=LWH
subsitute 4 for V, subsitute H for H and (10-4H)/(H+2) for W
V=(4)(H)(10-4H)/(H+2)
V=(40H-16H²)/(H+2)
find max value
take deritivitive of this thing
V'=-16(H²+4H-5)/((H+2)²)
using sign chart
sign changes from positive to negative at H=1
so at H=1
find W
W=(10-4H)/(H+2)
W=2
the dimeionts are
length=4ft
width=2ft
height=1ft
(the volume is 8 cubic feet)
Answer:
The matching is shown below.
Step-by-step explanation:
The given sets are defined as
A = {x | x < 1}
It means all the values of x which are less than 1.
B = {x | x ≥ 5}
It means all the values of x which are greater than or equal to 5.
C = {x | x = 5}
It means all the value of x is 5.
Union of two sets contains all the elements of both sets.
Intersection of two sets contains only common elements of both sets.
The matching is shown below.
Sets Correct value
1. A ∪ B {x | x < 1 or x ≥ 5}
2. A ∪ C {x | x < 1 or x = 5}
3. B ∪ C {x | x ≥ 5}
4. A ∩ B Ø
5. B ∩ C {x | x = 5}
Answer:
-1
Step-by-step explanation:
dy/dt = y² − 1 = (y + 1) (y − 1)
At t = 0, y = 0, and dy/dt = -1. Therefore, y is initially decreasing.
As y decreases, dy/dt increases. When y = -1, dy/dt = 0 and changes signs from negative to positive.
As y increases above -1, dy/dt again becomes negative. So y continues to approach -1 as t approaches infinity.
Answer:
$475
Step-by-step explanation:
998=x+y
y=48+x
graph
intersect at (475,523)
