![babyj93](/avatars/35860.jpg)
babyj93
19.08.2021 •
Mathematics
Margo bought the following lengths of ribbon: 3/4 yd, 1/3 yd, 1/2 yrd. How much ribbon did she buy?
Solved
Show answers
More tips
- S Style and Beauty How to choose the best mascara for your eyelashes...
- F Food and Cooking Discover Delicious Recipes You Can Make with Ground Meat...
- C Computers and Internet Google Search Tips and Tricks: Everything You Need to Know...
- S Science and Technology Why is there no gravity on other planets?...
- L Leisure and Entertainment How to Properly Wind Fishing Line onto a Reel?...
- L Leisure and Entertainment How to Make a Paper Boat in Simple Steps...
- T Travel and tourism Maldives Adventures: What is the Best Season to Visit the Luxurious Beaches?...
- H Health and Medicine Kinesiology: What is it and How Does it Work?...
- O Other How to Choose the Best Answer to Your Question on The Grand Question ?...
- L Leisure and Entertainment History of International Women s Day: When Did the Celebration of March 8th Begin?...
Answers on questions: Mathematics
- M Mathematics Complete this item. Identify 1 and 2. Select all that apply of the following terms: acute, right, obtuse, adjacent, vertical, complementary, supplementary.acuterightobtuseadjacentverticalcomplementarysupplementary...
- M Mathematics 54=__x6 Can anyone tell me...
- M Mathematics Enter a recursive rule and an explicit rule for the sequence. 7, 35, 175, 875,... A recursive rule for the sequence is f(1) = and f(n) = ,n2. An explicit rule for the sequence is...
- M Mathematics What is the lateral surface area of this cone?...
- M Mathematics Suppose the random variables X and Y have joint pdf as follows: f(x, y)=15xy2, 0 y x 1 a. Find the marginal pdf f1(x) of X. b. Find the conditional pdf f2(y | x). c. FindP(Y 1/3|X=x)forany1/3...
- M Mathematics A prism has a volume of 56. If the dimensions of the prism are tripled, what is the volume of the new prism? O A. 1512 O B. 504 O C. 168 O D. 2.07...
- M Mathematics Based on the sample of n = 25 healthy-weight students, can you conclude that healthy-weight students eat significantly fewer fatty, sugary snacks than the overall population? Use...
- M Mathematics How many pounds would u lose if u work out for 55 hours...
- M Mathematics What are the equations of the asymptotes of the graph of f(x)=4x+1+11 ? Select each correct answer....
- M Mathematics What is the height of a cylinder with a volume of 936x cubic inches and a diameter of 24 inches? 1.625 inches 4.75 inches 6.5 inches 39 inches...
Ответ:
the dimensions that will minimize the cost of constructing the box is:
a = 5.8481 in ; b = 5.848 in ; c = 10.234 in
Step-by-step explanation:
From the information given :
Let a be the base if the rectangular box
b to be the height and c to be the other side of the rectangular box.
Then ;
the area of the base is ac
area for the front of the box is ab
area for the remaining other sides ab + 2cb
The base of the box is made from a material costing 8 ac
The front of the box must be decorated, and will cost 10 ab
The remainder of the sides will cost 4 (ab + 2cb)
Thus ; the total cost C is:
C = 8 ac + 10 ab + 4(ab + 2cb)
C = 8 ac + 10 ab + 4ab + 8cb
C = 8 ac + 14 ab + 8cb ---- (1)
However; the volume of the rectangular box is V = abc = 350 in³
If abc = 350
Then b =![\dfrac{350}{ac}](/tpl/images/0714/5751/9e0d9.png)
replacing the value for c in the above equation (1); we have :
Differentiating C with respect to a and c; we have:
From (2)
From (3)
Replacing the value of a in 5 into equation (4)
From (5)
a = 5.8481
Recall that :
b =![\dfrac{350}{ac}](/tpl/images/0714/5751/9e0d9.png)
b =![\dfrac{350}{5.8481*10.234}](/tpl/images/0714/5751/2d25a.png)
b =5.848
Therefore ; the dimensions that will minimize the cost of constructing the box is:
a = 5.8481 in ; b = 5.848 in ; c = 10.234 in