Answer:
a. 8.4 ft³
b. 4.44 ft × 2.44 ft × 0.78 ft
Step-by-step explanation:
a. <em>Maximum volume
</em>
We are creating a box with dimensions
l = 6 – 2x
w = 4 – 2x
h = x
V = lwh = x(6 – 2x)(4 – 2x)
We must determine the value of x that makes V a maximum.
One way is to plot the function V = x(6 – 2x)(4 – 2x).
The maximum appears to be at about (0.78, 8.4).
Thus, the maximum volume is 8.4 ft³.
b.<em> Dimensions
</em>
l = 6 – 2 × 0.78 = 6 – 1.56 = 4.44 ft
w = 4 – 2 × 0.78 = 4 – 1.56 = 2.44 ft
h = 0.78 ft
The box with maximum volume has dimensions 4.44 ft × 2.44 ft × 0.78 ft.
Answer:
x=−3 or x=5
Step-by-step explanation:
x2−2x−15=0
Step 1: Factor left side of equation.
(x+3)(x−5)=0
Step 2: Set factors equal to 0.
x+3=0 or x−5=0
x=−3 or x=5
Answer:
a) ⅓ units²
b) 4/15 pi units³
c) 2/3 pi units³
Step-by-step explanation:
4y = x²
2y = x
4y = (2y)²
4y = 4y²
4y² - 4y = 0
y(y-1) = 0
y = 0, 1
x = 0, 2
Area
Integrate: x²/4 - x/2
From 0 to 2
(x³/12 - x²/4)
(8/12 - 4/4) - 0
= -⅓
Area = ⅓
Volume:
Squares and then integrate
Integrate: [x²/4]² - [x/2]²
Integrate: x⁴/16 - x²/4
x⁵/80 - x³/12
Limits 0 to 2
(2⁵/80 - 2³/12) - 0
-4/15
Volume = 4/15 pi
About the x-axis
x² = 4y
x² = 4y²
Integrate the difference
Integrate: 4y² - 4y
4y³/3 - 2y²
Limits 0 to 1
(4/3 - 2) - 0
-2/3
Volume = ⅔ pi
0,3,6,9,12,15,18,21,24,27,30,33,36
0,12,24,36
104 is the answer to your problem
