spycn5069
28.12.2019 •
Mathematics
Aclosed rectangular box is to constructed with a base that is twice as long as it is wide. if the total surface area is 27 square feet, find the dimensions of the box that maximize the volume.
Solved
Show answers
More tips
- S Science and Technology How to Restore the Diamond Shine to Your Tarnished Silverware...
- C Computers and Internet Boost your processor performance with these easy tips...
- L Leisure and Entertainment When will Maslenitsa start?...
- F Food and Cooking Discovering the Mysterious Fruit of Feijoa...
- B Business and Finance How to Open an Online Store? A Detailed Guide for Beginners...
- W Work and Career How to Write a Resume That Catches the Employer s Attention?...
- C Computers and Internet Е-head: How it Simplifies Life for Users?...
- F Family and Home How to Choose the Best Diapers for Your Baby?...
- F Family and Home Parquet or laminate, which is better?...
- L Leisure and Entertainment How to Properly Wind Fishing Line onto a Reel?...
Answers on questions: Mathematics
- M Mathematics Mrs.murray gave 60 cans to the food drive. 1 out of every 4 cans were soup cans. how many donated cans were soup cans? answers are above! ☝☝...
- M Mathematics Why would a sin be positive...
- M Mathematics Millie is drawing a triangle. One side has a length of 9 units, and another side has a length of 6 units. What could be the length of the third side of the triangle?...
- M Mathematics [(23 × 2.5) , 1/2] + 120...
- M Mathematics Pls help Solve for m a=f/m...
- M Mathematics AHHHHHH AGAIN!? so someone helped me understand how to do long division again! ty, i just need to know... what is this? ima give the crown again for this one as well (also...
- M Mathematics The Thompson family made this table when finding their net worth. Use this table to answer the question....
- M Mathematics X intercept of y = -3x + 3...
- M Mathematics A number m plus 4 is greater than or equal to 7 O m +4 7 Om + 4 7 Om + 4 7 ...
- M Mathematics PLEASE ANSWER QUICK!! in ms. renault s classroom, 3/5 of the students play chess. of the students who play chess, 5/6 also play checkers. if there are 30 students in her class,...
Ответ:
For maximum volume the dimension should be;
w= 1.5ft , b=3ft and h= 2ft
Step-by-step explanation:
The surface area of the rectangular box
S = 2wb + 2wh + 2bh = 27ft^2 1
Given that b = 2w
Substituting into eqn 1
2w(2w) + 2wh + 2h(2w) = 27
4w^2 + 2wh + 4hw = 27
h(6w) = 27 - 4w^2
h = (27 - 4w^2)/6w 2
The volume of a rectangular box is given as
V=w×b×h
V= w×2w×h = 2hw^2 3
Substituting eqn2 into eqn3
V=2w^2(27-4w^2)/6w
V = w(27-4w^2)/3 = (27w-4w^3)/3
To find the maximum point, we need to differentiate the eqn above.
At maximum dV/dw = 0
dV/dw = (27 - 12w^2)/3 = 0
12w^2 = 27
w^2 = 9/4
w = 3/2ft = 1.5ft
b = 2w = 6/2 = 3ft
h = (27 - 4w^2)/6w
h = (27 - 4(3/2)^2)/6(3/2)
h = ( 27 - 9)/6 = 18/9
h = 2ft
Ответ:
I think it's a 96 i hope you find this helpful and goodluck;)
Step-by-step explanation: