![vaelriacb5317](/avatars/10821.jpg)
vaelriacb5317
07.01.2020 •
Mathematics
find the dimensions of a box with a square base with
(a) volume 12 and the minimal surface area
(b) surface area 20 and minimal volume
Solved
Show answers
More tips
- F Food and Cooking What to Give as a Wedding Gift?...
- F Food and Cooking Everything You Need to Know About Pasta...
- C Computers and Internet How to Choose a Monitor?...
- S Style and Beauty How to Get Rid of Peeling Nails: Natural Remedies...
- S Science and Technology Understanding Magnetic Storms: A Guide to This Natural Phenomenon...
- F Family and Home What is Most Important in Men s Lives?...
- G Goods and services Which TV is better - LCD or Plasma?...
- C Computers and Internet Are there special gaming mice?...
- G Goods and services LED-подсветка в LCD-телевизорах: 5 причин, почему она лучше других технологий...
- C Computers and Internet Keep Your Mouse Pad Clean: The Right Way to Clean It?...
Answers on questions: Mathematics
- M Mathematics Let a=x squared+4. use a to find the solutions for the following equation: (x squared + 4) squared+ 32= 12x squared+ 48 what are some solutions for x? -8, -2, 4, 0, 2, -4,...
- M Mathematics Kelly sells lamps. she marks them down 17%. write two expressions to represent the sale price. let (c) represent the original cost of the lamp....
- M Mathematics Mrs. adams buys for bananas and six apples. what is the ratio of bananas to apples?...
- M Mathematics Luna want to know what proportion of the 7th graders at her school are interested in taking art class. which is the best group survey to find this information. a: ask all of...
- M Mathematics The death of a swimming pool is 8.5 meters what is half of the depth in millimeters...
- M Mathematics What is 1/4 shaded of 8 piece bar graph...
- M Mathematics Can someone me with this for 30 points...
- M Mathematics If possible, find a solution to tan(6θ+5)=−8. if no solution exists, enter none....
- M Mathematics What is 69×69×69×69 im in 6th grade im in class have a pop quiz...
- M Mathematics After conducting a survey of all his classmates, luke discovers that the amount of money everyone spends buying snacks each month has a mean of $38. what does the mean say...
Ответ:
A box has a square base of side x and height y where x,y > 0.
Its volume is V = x^2y and its surface area is S = 2x^2 + 4xy.
(a) If V = x^2y = 12, then y = 12=x^2 and S(x) = 2x^2 C 4x (12=x2) = 2x2 + 48x^-1. Solve S'(x) = 4x - 48x-2 = 0 to obtain x = 12^1/3. Since S(x/) ---> infinite as x ---> 0+ and as x --->infinite, the minimum surface area is S(12^1/3) = 6 (12)^2/3 = 31.45, when x = 12^1/3 and y = 12^1/3.
(b) If S = 2x2 + 4xy = 20, then y = 5^x-1 - 1/2 x and V (x) = x^2y = 5x - 1/2x^3. Note that x must lie on the closed interval [0, square root of 10]. Solve V' (x) = 5 - 3/2 x^2 for x>0 to obtain x = square root of 30 over 3 . Since V(0) = V (square root 10) = 0 and V(square root 30 over 3) = 10 square root 30 over 9 , the maximum volume is V (square root 30 over 3) = 10/9 square root 30 = 6.086, when x = square root 30 over 3 and y = square root 30 over 3 .
Ответ:
idk
Step-by-step explanation: