1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Elis [28]
1 year ago
12

Using differential calculus, maximize the volume of a box made of cardboard (top is open) as shown in Figure A. 15, subject to t

he following constraints. 1. Allowable area of the cardboard is equal to 40 in^2. 2. The length of the box L is equal to its width W.
Mathematics
1 answer:
lana [24]1 year ago
3 0

The maximum volume of the box is 40√(10/27) cu in.

Here we see that volume is to be maximized

The surface area of the box is 40 sq in

Since the top lid is open, the surface area will be

lb + 2lh + 2bh = 40

Now, the length is equal to the breadth.

Let them be x in

Hence,

x² + 2xh + 2xh = 40

or, 4xh = 40 - x²

or, h = 10/x - x/4

Let f(x) = volume of the box

= lbh

Hence,

f(x) = x²(10/x - x/4)

= 10x - x³/4

differentiating with respect to x and equating it to 0 gives us

f'(x) = 10 - 3x²/4 = 0

or, 3x²/4 = 10

or, x² = 40/3

Hence x will be equal to 2√(10/3)

Now to check whether this value of x will give us the max volume, we will find

f"(2√(10/3))

f"(x) = -3x/2

hence,

f"(2√(10/3)) = -3√(10/3)

Since the above value is negative, volume is maximum for x = 2√(10/3)

Hence volume

= 10 X 2√(10/3)  -  [2√(10/3)]³/4

= 2√(10/3) [10 - 10/3]

= 2√(10/3) X 20/3

= 40√(10/27) cu in

To learn more about Maximization visit

brainly.com/question/14682292

#SPJ4

Complete Question

(Image Attached)

You might be interested in
Name the set(s) of numbers to which -10 belongs.
NeX [460]
-10 belongs to integers, rational numbers, and real numbers.
6 0
3 years ago
Read 2 more answers
Two companies Company A and Company B offer the same starting salary of $20,000 per year. Company A gives a raise of $1000 each
Bingel [31]
A.) A = 20000 + 1000n
B = 20000(1.04)^n

b.) For A, sn = n/2(2a + (n - 1)d)
s20 = 20/2(2(20000) + 1000(20 - 1)) = 10(40000 + 19(1000)) = 10(40000 + 19000) = 10(59000) = $590,000
For B, sn = a(r^n - 1)/(r - 1)
s20 = 20000((1.04)^20 - 1)/(1.04 - 1) = 20000(2.191 - 1)/0.04 = 20000(1.191)/0.04 = 23822.46 / 0.04 = $595,561.57

c.) Using a graphing calculator, it takes 18 years for the
<span>total amount earned a company B is greater that the total amount of earned at company A.</span>
5 0
3 years ago
Pleaseeee helpppp!!!!​
kondor19780726 [428]

The right answer is Option A:x=\frac{rs-t}{2}

Step-by-step explanation:

Given expression is;

s=\frac{2x+t}{r}

We will solve this expression for x, therefore,

Multiplying both sides by r

r*s=\frac{2x+t}{r}*r\\rs=2x+t

Subtracting t from both sides

rs-t=2x+t-t\\rs-t=2x\\2x=rs-t

Dividing both sides by 2

\frac{2x}{2}=\frac{rs-t}{2}\\x=\frac{rs-t}{2}

The right answer is Option A:x=\frac{rs-t}{2}

Keywords: subtraction, division

Learn more about subtraction at:

  • brainly.com/question/1238144
  • brainly.com/question/12497249

#LearnwithBrainly

7 0
3 years ago
What should be the paper weight
nata0808 [166]

Answer:

6.25 cm

Step-by-step explanation:

\rho=\dfrac{m}{V} \\\\V_{\text{pyramid}}= A_{\text{base}}\cdot h \cdot \dfrac{1}{3} \\\\1.6=\dfrac{400}{V} \\\\V=120 \cdot h \cdot \dfrac{1}{3} \\\\1.6=\dfrac{400}{40h} \\\\1.6=\dfrac{10}{h} \\\\1.6h=10 \\\\h=\dfrac{10}{1.6}=6.25\text{ cm}

Hope this helps!

8 0
3 years ago
Read 2 more answers
Marking Brainliest ! Answer quickly
Alex

Answer:

5/7

Step-by-step explanation:

20/28=5/7

Hoped i answered u

4 0
3 years ago
Read 2 more answers
Other questions:
  • Please help and thank you
    5·1 answer
  • WHOEVER GETS IT RIGHT FIRST WILL BE CHOSEN THE BRAINLIEST!!
    8·2 answers
  • Use the Quadratic Formula to find the exact solutions of x2 + 7x − 4 = 0. x equals negative b plus or minus the square root of b
    6·2 answers
  • 10 pol
    8·1 answer
  • Kimmy has 47 ft.² of cement blocks each square block has size 1 foot long what is the greatest perimeter of a rectangle that she
    12·1 answer
  • HELP!!! WILL GIVE BRAINLIEST!!!!
    8·1 answer
  • Which planet in the chart is most likely Earth? Yeah <br> Does somone no the answer
    13·1 answer
  • PLEASE Help mE wiTh the two QUESTIONS
    13·1 answer
  • Can someone help me pls
    13·2 answers
  • I dont understand if anybody can help me i would be happy​
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!