Answer:
x = 2.354 in
Maximum volume = 228.162 in³
Step-by-step explanation:
Size of the metal sheet = (18 in × 12 in)
Let the height of the box = x in
Then length of the box = (18 - 2x) in
Width of the box = (12 - 2x) in
Now volume of the rectangular box (V) = Length × Width × height
= (18 - 2x) × (12 - 2x) × x
= x[18(12 - 2x) - 2x(12 - 2x)]
= x[216 - 36x - 24x + 4x²]
= x[216 - 60x + 4x²]
= (4x³ - 60x² + 216x) in³
For maximum volume, we will find the derivative of the volume and equate it to zero.
V' = 12x² - 120x + 216
V' = 0
12x² - 120x + 216 = 0
x² - 10x + 18 = 0
By quadratic formula,
x =
x = 5 ± √7
x = 7.646, 2.354
But for 7.646, volume of the box will be negative.
Therefore, (x = 2.354 in) will be value of x for maximum volume of the box.
Maximum volume of the box = 4(2.354)³ - 60(2.354)² + 216(2.354)
= 228.162 in³
h(t) = -16t² + 50t + 5
The maximum height is the y vertex of this parabola.
Vertex = (-b/2a, -Δ/4a)
The y vertex is -Δ/4a
So,
The maxium height is -Δ/4a
Δ = b² - 4.a.c
Δ = 50² - 4.(-16).5
Δ = 2500 + 320
Δ = 2820
H = -2820/4.(-16)
H = -2820/-64
H = 2820/64
H = 44.0625
So, the maxium height the ball will reach is 44.0625
Answer: $ 1.50
Step-by-step explanation:
Sorry if I’m wrong
The equation would be y = 3/5x + 3
.8, 1.8, 8, 8.1
Do you understand why? This seems pretty simple that you should be able to solve this for yourself.