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
Licemer1 [7]
2 years ago
14

It’s time to lock down the design details for the redesigned Brick and Egyptian candles. Because of manufacturing constraints, t

he base length for each candle has to be at least 2 cm and can be no more than 10 cm. Make a recommendation for the base dimensions of each candle. Explain how you determined your base dimensions. Your reasoning does not have to be all math related.
Mathematics
1 answer:
Delvig [45]2 years ago
6 0

Answer:

THE SMALLEST FORMS:

- smallest prism ---> the cube with all sides 2 ==> the volume is 2*2*2 = 8 cm^3

- smallest pyramid number one ---> the pyramid with base sides 2 and the height also 2 ==> the volume is (1/3)*2*2*2 = 8/3 cm^3

- smallest pyramid number two ---> the pyramid with base sides 2 and the lateral sides also 2 ==> the radius of the base is sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 2^2 - sqrt(2)^2 = 4 - 2 = 2 ==> pyramid_height = sqrt(2) ==> the volume is (1/3)*2*2*sqrt(2) = 4*sqrt(2)/3 cm^3

- smallest cylinder --> the cylinder of diameter 2 and height also 2 ==> the radius is diameter/2 = 2/2 = 1 ==> the volume is pi*(radius^2)*height = pi*(1^2)*2 = pi*1*2 = 2*pi cm^3

The lesser volume is the volume of the smallest pyramid number two. ==> it's wax cost is approximately 0.0075 * 4 * 1.42 / 3 $ per candle = 0.014 $ per candle ==> the total cost  per candle is approximately 0.014 + 1.6 = 1.614 $ per candle.

THE BIGGEST FORMS:

- biggest prism ---> the cube with all sides 10 ==> the volume is 10*10*10 = 1000 cm^3

- biggest pyramid number one ---> the pyramid with base sides 10 and the height also 10 ==> the volume is (1/3)*10*10*10 = 1000/3 cm^3

- biggest pyramid number two ---> the pyramid with base sides 10 and the lateral sides also 10 ==> the radius of the base is 5*sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 10^2 - [5*sqrt(2)]^2 = 100 - 50 = 50 ==> pyramid_height = 5*sqrt(2) ==> the volume is (1/3)*10*10*5*sqrt(2) = 500*sqrt(2)/3 cm^3

- biggest cylinder --> the cylinder of diameter 10 and height also 10 ==> the radius is diameter/2 = 10/2 = 5 ==> the volume is pi*(radius^2)*height = pi*(5^2)*10 = pi*25*10 = 250*pi cm^3

The bigger volume is the volume of the biggest prism (the side-10 cube). ==> it's wax cost is  0.0075 * 1000 $ per candle = 7.5 $ per candle ==> the total cost per candle is 7.5 + 1.6 = 9.1 $ per candle

The range of the cost is the interval [1.614 ; 9.1]. Depending on other prices on the market,  you greed, and other factors you will put a profit margin: maybe 20% of the cost ; maybe a fixed margin like 5$. So the price per candle will be the cost per candle plus the profit margin per candle.

If I were to choose the base length I would have to say 6 because it is the arithmetic mean between 2 and 10: (2+10)/2 = 12/2 = 6. 2cm is too small, and 10cm is too big.

Also if you start with a rectangle of length 10 and width 2 and you have to find the rectangle with the largest area by being allowed to increase the width and decrease the width with the same quantity you get this:

Area of the new rectangle is (10-x)(2+x) = -x^2 + 8x + 20 = -x^2 + 8x -16 + 36 = -(x^2 - 2*x*4 + 4^2) + 36 = -(x-4)^2 + 36 = 36 - (x-4)^2 which has the maximum value of 36 because out of 36 you subtract a positive value. You get the maximum when (x-4)^2 = 0 ==> x-4=0 ==> x=4

The new length is 10-4=6 and the new width is 2+4=6.

Next I would choose the height of the prism (I like prisms :P) to be [the_golden_ratio]*[base_side] which is approximately 1.618 * 6 = 9.708 which I would round up to 10. ==> The volume would be 6*6*10 = 360 cm^3. ==> the cost would be 0.0075*360 + 1.6 = 2.7 + 1.6 = 4.3 $ per candle. And because my candle is so perfect I'd put the profit margin to be 5.69 $ per candle so I can proudly show it in the store with the price of 4.3 + 5.69 = 9.99 $ :)

You might be interested in
Select all of the ordered pairs (x,y) that are solutions to the linear equation 2x+3y=6.
Romashka-Z-Leto [24]

Answer: (0,2), (3,0), (6, -2)

6 0
2 years ago
PLEASE HELP!!!!!!!!!!!!!!!!
soldier1979 [14.2K]

Answer:

For the first one about Jack the answer to A is 14, 21, 30 and for b the answer is 22. Now for Maria the answer for A is 24 , 40 , 80 and for b it's 8

Step-by-step explanation:

All you had to do for Jack was just add 10 to each number that's for A Now for B you just had to minus ( - ) 10 from 32 which equals 22. For Maria You needed to times ( × ) every number from 4 .

7 0
2 years ago
Write the following number in standard decimal form.
Anestetic [448]

Answer: 6.534 x 10^(-1)

Step-by-step explanation:

Six thousand five hundred and thirty four ten thousandth

6534/10000

Convert to decimal

6534/10000=0.6534

Then convert to standard form

0.6534=6.534 x 10^(-1)

4 0
3 years ago
Which expression is not equivalent to the
9966 [12]

Answer:

D: 6y+3+5y-2

Step-by-step explanation:

6y+3+5y-2 = 11y + 1

All the other expressions evaluate, after simplification to 11y+5

6 0
1 year ago
Which is the same as moving the decimal point 3 places to the left in decimal number?
oksano4ka [1.4K]
Multiply it by -1000
7 0
2 years ago
Other questions:
  • Which of the binomials below is a factor of this trinomial?
    15·1 answer
  • How to factorize<br><br> a)x³-4x<br><br> b) 9t²-u²<br><br> hurry up
    13·2 answers
  • How do you solve -26d = -364?
    9·2 answers
  • Tom and Bob have a total of 49 toys if Bob has 5 more toys than Tom, how many toys does each one have
    12·2 answers
  • Simon neatly arranged 35 radio controlled cars in 5 rows on the shelf find the number of cars placed in each row
    9·1 answer
  • in ten years, the population increases from 20,000 to 23,000. Find the actual increase and the percentage increase.
    7·2 answers
  • Enter the decimal 1.45 as an improper fraction in simplest form.
    15·2 answers
  • PLS HELP !!! U WILL GET 13 POINTS AND BRAINLIEST !!THIS IS A TEST AND I NEED TO SHOW WORK PLS PLS HELP AND ONLY ANSWER IF U KNOW
    5·1 answer
  • Amanda's parents had a birthday dinner for her at Sushi Yama restaurant. The bill came to $74 before the tip. They left an 18% t
    10·1 answer
  • If you sell $1000 worth of popcorn, then your Boy Scout dues are free. Ethan sold $1000 worth of popcorn. Conclusion: Ethan's Bo
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!