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
Bogdan [553]
3 years ago
7

A 1,000 gallon pool (no top) with a rectangular base will be constructed such that the length of the base is twice the width. Fi

nd the dimensions (length, width, and height) of the pool that minimize the amount of material needed to construct it.
Mathematics
1 answer:
Yuliya22 [10]3 years ago
5 0

Answer:

W = 4.646 ft

L = 9.292 ft

H = 3.097 ft

Step-by-step explanation:

Let's say the L is the length, W is the width, and H is the height.

The volume of the pool is:

V = LWH

The area of the pool is:

A = LW + 2LH + 2WH

L = 2W, so substituting:

V = (2W)WH

V = 2W²H

A = (2W)W + 2(2W)H + 2WH

A = 2W² + 4WH + 2WH

A = 2W² + 6WH

Solving for H in the first equation and substituting into the second:

H = V/(2W²)

A = 2W² + 3V/W

Find dA/dW and set to 0.

dA/dW = 4W − 3V/W²

0 = 4W − 3V/W²

4W = 3V/W²

4W³ = 3V

W = ∛(¾V)

V = 1000 gallons or 133.7 ft³.

W = ∛(¾(133.7 ft³))

W = 4.646 ft

So L = 9.292 ft and H = 3.097 ft.

You might be interested in
WILL GIVE BRAINLIEST PLEASE ADD THE REASONING PART!!
nasty-shy [4]

Answer:

new price= $2.40

Step-by-step explanation:

20%= 20/100= 1/5

$3.00/5= 00.60

1/5 of the price is being subtracted from $3.00

$00.60 is 1/5

3.00-.60= 2.40

3 0
2 years ago
Read 2 more answers
a bag contains 6 black marbles and 6 white marbles. What is the least number of marbles that you must choose, without looking, t
o-na [289]

Given:

Number of black marbles = 6

Number of white marbles = 6

Let's determine the least number of marbles that can be chosen to be certain that you have chosen two marble of the same color.

To find the least number of marble to be chosen to be cartain you have chosen two marbles of the same color, we have:

Total number of marbles = 6 + 6 = 12

Number of marbles to ensure at least one black marble is chosen = 6 + 1 = 7

Number of marbles to ensure at least one white marble is chosen = 1 + 6 = 7

Therefore, the least number of marbles that you must choose, without looking , to be certain that you have chosen two marbles of the same color is 7.

ANSWER:

7

6 0
1 year ago
Justine runs 250 yards in 50 seconds.
DaniilM [7]

Answer:

a: 300 Yards

b: 10 seconds

c: 5 Yards per second

7 0
3 years ago
X^2-7x=0 solve the equation​
inn [45]

Answer:

x = 0, 7

Step-by-step explanation:

Step 1: Write out equation

x² - 7x = 0

Step 2: Factor out <em>x</em>

x(x - 7) = 0

Step 3: Find roots

x = 0

x - 7 = 0

x = 7

6 0
3 years ago
Read 2 more answers
PLEASE ANSWER!! I WILL GIVE BRAINIEST TO WHOEVER ANSWERS THIS FIRST!!!!!!!!!!!!!!!!!!!!!!!!!!!
hammer [34]
96 Square inches because if you multiply every side with each length you get 96 in2
6 0
3 years ago
Read 2 more answers
Other questions:
  • Solve the equation<br><br> -12 = x - 1 + 28
    10·2 answers
  • Which relationship exists between the two angles? What is the value of x? Find the measure of each angle. A) vertical angles; x
    15·2 answers
  • On B would it be X over 0.001?
    12·1 answer
  • Will a stand that can hold up to 40 pounds support a 21 kilogram television
    10·2 answers
  • PLSSS HELP WILL MARK BRANLIEST!!
    6·1 answer
  • Please help me :( ..​
    11·1 answer
  • Which mathematical concept did you use to find the number of gumballs that fit INSIDE the package?
    12·1 answer
  • which of the following equation represents a linear function a. f(x) =6x-3 b. f(x) = 7x(x+1) c.f(x) = x2+3x2 d. f(x) = x2(x-3​
    10·1 answer
  • 8^x=2 what is the value of x
    5·1 answer
  • Given that ​3x^2-3x+2 find each of the following. ​a) ​g(0) ​b) ​g(​) ​c) ​g(​) ​d) ​g(​x) ​e) ​g(1​t)
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!