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
Stella [2.4K]
3 years ago
5

An aquarium with a square base has no top. There is a metal frame. Glass costs 8 dollars/m^2 and the frame costs 7 dollars/m. Th

e volume is to be 20 m^3. Express the total cost C in terms of the height h in meters. (Hint: work out the cost of the glass and frame separately.)
Mathematics
1 answer:
Irina-Kira [14]3 years ago
3 0
Given that the volume of the aquarium is 20m^3.

Volume = Area of Base x height

Area of Base = Volume / height = 20/h

Given that the aquarium has a square base.

Area of square = l^2

Thus, the length of the base of the aquarium is \sqrt{area \ of \ base} = \sqrt{ \frac{20}{h} }

The frame is to cover 8 sides with the length equal to the length of the base and 4 sides with the length of the height.

Thus, the total perimeter of the frame is given by 8\sqrt{\frac{20}{h}}+4h= \sqrt{64\left(\frac{20}{h}\right)}+4h = \sqrt{\frac{1,280}{h}}+4h

Area of the four side faces of the aquarium is 4 times the length of the base times the height = 4\times\sqrt{ \frac{20}{h} }\times h=\sqrt{16\left(\frac{20}{h}\right)h^2}=\sqrt{320h}

Total area to be covered by grass is the base and the four side faces and is given by \frac{20}{h}+\sqrt{320h}

Cost of the entire metal frame = 7\left(\sqrt{\frac{1,280}{h}}+4h\right)= \sqrt{49\left(\frac{1,280}{h}\right)}+7(4h) = \sqrt{\frac{62,720}{h}}+28h

Cost of the entire grass = 8\left(\frac{20}{h}+\sqrt{320h}\right)=\frac{160}{h}+\sqrt{64(320h)}=\frac{160}{h}+\sqrt{20,480h

Therefore, total cost in terms of the height, h, is given by

C=\sqrt{\frac{62,720}{h}}+28h+\frac{160}{h}+\sqrt{20,480h
You might be interested in
A restaurantis planning to make changes to its menu. In order to decide which potential menu items are most popular with the cit
Alex

Answer:

Simple random sampling survey method

Step-by-step explanation:

A simple random sampling is an unbiased survey technique Hence it will represent all the parts of the city's population.

In statistics, a simple random sample is a subset of individuals (a sample) chosen from a larger set (a population). Each individual is chosen randomly and entirely by chance, such that each individual has the same probability of being chosen at any stage during the sampling process

6 0
3 years ago
7) You can buy 5 cans for green beans at the Village Market for $3.20. You can buy 10
Bad White [126]
Sam’s club because with the deal each can would be about $1.27 whereas at village market each can would be about $1.56
5 0
3 years ago
Find the quotient of the following 95 divide 13?
stira [4]

Answer:

6.3

Step-by-step explanation:

3 0
3 years ago
<img src="https://tex.z-dn.net/?f=99%20x%2012%20-%204" id="TexFormula1" title="99 x 12 - 4" alt="99 x 12 - 4" align="absmiddle"
telo118 [61]

Answer:

So long senior

Step-by-step explanation:

7 0
2 years ago
Let ​ x2+11x=3 ​.
frutty [35]
Add (11/2)^2 to both sides
x^2 + 11x + (11/2)^2 = 3 + (11/2)^2
x^2 + 11x + (11/2)^2 = 133/4
(x + 11/2)^2 = 133/4
x + 11/2 = sqrt of (133/4)
Solutions are
x = (sqrt of (133) - 11))/2
x = (-sqrt of (133) -11))/2
3 0
3 years ago
Read 2 more answers
Other questions:
  • Divide £21 in ratio 3:4
    11·1 answer
  • Hi again I’ll appreciate it if you help me
    8·1 answer
  • You scored 18 out of the 60 points scored by your team. what percent of your team's points did you score?70%30%
    8·2 answers
  • Write the expression as a square of a monomial. 4/9b^6
    13·1 answer
  • I need to get the answers for the blanks
    9·1 answer
  • 3 = −2∣ 1 — 4 s − 5 ∣ + 3
    13·1 answer
  • Assume that the empirical rule is a good model for the time it takes for all passengers to board an airplane. The mean time is 4
    13·1 answer
  • Find the rate of change of the area of a square with respect
    15·1 answer
  • The graph of a linear function is shown.
    5·1 answer
  • in my fish tank the ratio of the redfish to bluefish is 3:5 there are 20 bluefish how many red fish are there
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!