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
mars1129 [50]
2 years ago
13

An open metal tank of square base has a volume of 123 m^3

Mathematics
1 answer:
snow_lady [41]2 years ago
3 0

Answer:

  a) h = 123/x^2

  b) S = x^2 +492/x

  c) x ≈ 6.27

  d) S'' = 6; area is a minimum (Y)

  e) Amin ≈ 117.78 m²

Step-by-step explanation:

a) The volume is given by ...

  V = Bh

where B is the area of the base, x^2, and h is the height. Filling in the given volume, and solving for the height, we get:

  123 = x^2·h

  h = 123/x^2

__

b) The surface area is the sum of the area of the base (x^2) and the lateral area, which is the product of the height and the perimeter of the base.

S=x^2+Ph=x^2+(4x)\dfrac{123}{x^2}\\\\S=x^2+\dfrac{492}{x}

__

c) The derivative of the area with respect to x is ...

S'=2x-\dfrac{492}{x^2}

When this is zero, area is at an extreme.

0=2x -\dfrac{492}{x^2}\\\\0=x^3-246\\\\x=\sqrt[3]{246}\approx 6.26583

__

d) The second derivative is ...

S''=2+\dfrac{2\cdot 492}{x^3}=2+\dfrac{2\cdot 492}{246}=6

This is positive, so the value of x found represents a minimum of the area function.

__

e) The minimum area is ...

S=x^2+\dfrac{2\cdot 246}{x}=(246^{\frac{1}{3}})^2+2\dfrac{246}{246^{\frac{1}{3}}}=3\cdot 246^{\frac{2}{3}}\approx 117.78

The minimum area of metal used is about 117.78 m².

You might be interested in
Give me Colonel Sanders' Kentucky Fried Chicken.
bixtya [17]

Answer:

kk where do you live lol

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Chris is painting a wall with a length of 3 meters and a width of 1.6 meters
neonofarm [45]
Ok, so...what is the question?...
4 0
3 years ago
Becky orders pens from an office supply company. The table shows how many pens have black ink based on the total number of pens
dedylja [7]

Answer:

Step-by-step explanation:

6 0
2 years ago
X3 − 6x2 − 7x + 60 = 0
inna [77]
An equation ........
4 0
3 years ago
Katy has 46 missing assignments in math class and 60 missing assignments in history. She has 106 missing assignments in total. K
guapka [62]

Answer:

She needs to do at least 8 a day

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Other questions:
  • What number is 7 units to the left of -1?<br><br> 6<br> -6<br> -8<br> 8
    8·2 answers
  • Daily pie special choice of 1 of 3 pies and choice of 1 of 4 drinks how many ways can you order
    7·1 answer
  • You can work no more than 60 hours each week at your two jobs. Dog walking pays $7 per hour and your sales job at Computers &amp
    10·2 answers
  • 2/7 divided by 1 2/7
    11·1 answer
  • Find this awnser and ur the best​
    14·1 answer
  • −6x+2x−5+2: simplified
    14·1 answer
  • Solve for the inequality ᵏ⁄₄ ≥ 6
    8·2 answers
  • WILL GIVE BRAINLIEST; I NEED ANSWERS ASAP
    7·1 answer
  • A population of cheetahs has decreased 30% over the last 18 years if they're originally about 12,000 cheetahs how many cheetahs
    11·1 answer
  • Alex wants to buy cupcakes for his work office but also does not want to spend over $25 because he doesn't like his co workers *
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!