SOLUTION:
A box has a square base of side x and height y where x,y > 0.
Its volume is V = x^2y and its surface area is
S = 2x^2 + 4xy.
(a) If V = x^2y = 12, then y = 12=x^2 and S(x) = 2x^2 C 4x (12=x2) = 2x2 + 48x^-1. Solve S'(x) = 4x - 48x-2 = 0 to
obtain x = 12^1/3. Since S(x/) ---> infinite as x ---> 0+ and as x --->infinite, the minimum surface area is S(12^1/3) = 6 (12)^2/3 = 31.45,
when x = 12^1/3 and y = 12^1/3.
(b) If S = 2x2 + 4xy = 20, then y = 5^x-1 - 1/2 x and V (x) = x^2y = 5x - 1/2x^3. Note that x must lie on the closed interval [0, square root of 10]. Solve V' (x) = 5 - 3/2 x^2 for x>0 to obtain x = square root of 30 over 3 . Since V(0) = V (square root 10) = 0 and V(square root 30 over 3) = 10 square root 30 over 9 , the
maximum volume is V (square root 30 over 3) = 10/9 square root 30 = 6.086, when x = square root 30 over 3 and y = square root 30 over 3 .
Answer:
<h2>====LEARN WITH REY====</h2>
What property can I use for this question: 3x57
In this property there is the property of the multiplication part
Step-by-step explanation:
If calculated, the result is
3 x 57 = 171
<h3>
#Study with brainly </h3><h3>
# Learn with rey</h3>
<h3>
Question code : 5.2.7</h3><h3>
Course : Math</h3><h3>
Theory : Splash</h3>
Answer:
(
0
,
5
)
,
(
1
,
3
)
(
2
,
1
)
Step-by-step explanation:
1. x=0
y=-2(0)+5
y=5
(
0
,
5
)
2. x=1
y=-2(1)+5
y=-2+5
y=3
(
1
,
3
)
3. x=2
y=-2(2)+5
y=-4+5
y=1
(
2
,
1
)
Use the formula A= height*base/2
