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
Paha777 [63]
2 years ago
10

A factory makes light fixtures with right regular hexagonal prisms where the edge of a hexagonal base measures 4 cm and the leng

ths of the prisms vary. It cost $0.04 per square centimeter to fabricate the prisms and the factory owner has set a limit of $11 per prism. What is the maximum length of each prism?
Mathematics
1 answer:
chubhunter [2.5K]2 years ago
6 0

The maximum length of the prism is highest length of the hexagonal prism

The maximum length of each prism is 8.0 cm

<h3>How to determine the maximum length of each prism?</h3>

The surface area of the hexagonal prism is calculated using:

A = 6al + 3\sqrt3 a^2

Where:

a represents the edge length; a = 4 cm

l represents the length (or height) of the prism

The surface area costs $0.04 per square centimeter.

So, we have:

C = 0.04 * [6al + 3\sqrt3 a^2]

The maximum cost is $11.

So, the equation becomes

11 = 0.04 * [6al + 3\sqrt3 a^2]

Substitute 4 for a

11 = 0.04 * [6 * 4l + 3\sqrt3 * 4^2]

Evaluate the products and exponents

11 = 0.04 * [24l + 48\sqrt3]

Divide both sides by 0.04

275 = 24l + 48\sqrt3

Subtract 48\sqrt3 from both sides

24l = 275 - 48\sqrt3

Evaluate the difference

24l = 191.9

Divide both sides by 24

l = 8.0

Hence, the maximum length of each prism is 8.0 cm

Read more about surface areas at:

brainly.com/question/6613758

You might be interested in
14) The number of students at LAMS is 1872 students. The ratio of girls to
bogdanovich [222]

Answer:

310

Step-by-step explanation:

total no.of students=1872

ratio of boys to girls=7:5

sum of ratio=total of students

12/12=1872

7/12=?

7/12*1872/1=1092which is the number of girls

1872-1092=780which is the number of boys

difference =1092-780= 310

7 0
3 years ago
The graph shows the function f(x) = |x-h[ + k. What is
Olegator [25]

Answer:

K=-2.5

Step-by-step explanation:

because the line is in the middle of 2 and 3 and is below which means that it is negative

8 0
3 years ago
Read 2 more answers
Which expressions are equivalent to the one below? Check all that apply.<br> 3x
noname [10]

Answer:

F and C

Step-by-step explanation:

5 0
3 years ago
Triangle with base of 12 and height of 10. what is the other number?????????
victus00 [196]
120 is the other number. 
6 0
3 years ago
I need these answers ​
AVprozaik [17]

Answer:

You are correct with all of your answers so far,...

Step-by-step explanation:

5) = 0 (-17 + 20 = 3,... 3 + -3 = 0)

6) = -34 (-34 + 25 = -9,... -9 + -25 = -34)

9) = -4 (7 + -11 = -4)

Chow,...!

4 0
3 years ago
Read 2 more answers
Other questions:
  • S = ut+ 16t²<br>Find the value of s when u = 2 and t = 3.​
    14·2 answers
  • A metal cube
    10·1 answer
  • - 2/x = 3/6 please answer this question
    7·1 answer
  • Rectangle ABCD has vertices at coordinates (0,8), (4,12), (12,4), and D, respectively. Which of the following correctly identifi
    12·1 answer
  • What is the value of x in the equation 3(2x + 8) = 0? (4 points)
    10·1 answer
  • "If you have 2 pieces of spaghetti that have lengths 4 cm and 10 cm, what could be the possible length of a third piece of spagh
    8·1 answer
  • Robin has a piece of ribbon that is 4.5 meters long. She wants to cut it into pieces that are .05 meters long. How many pieces o
    6·2 answers
  • In parallelogram RSTU if RT=36 find RV.
    6·2 answers
  • Identify the equation in slope-intercept form for the line containing the point (2,1) and parallel to y=5/3x−1/3.
    6·1 answer
  • What is this symbol??​
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!