I need help figuring out the dimensions of the table top. I attached the problem as well as the work I have done The table aquarium shown above holds 70 gallons of water. The tank has a square base and the top extends4 inches past each side. Suppose the amount of glass used to build the aquarium tank is optimized, howmuch glass was needed to build this aquarium? What are the dimensions of the tank? What are thedimensions of the tabletop?Your group is to write a report that explains your findings. The report must include the following:• Submit one project/report per group. Be sure to include everyone's names, first and last.• Restate each question and clearly explain how you found the solution.1st and 2nd derivative tests to solve the problem and justify your work.• Graphs of the 1 and 2nd derivatives with important points labeled.Concluding paragraph.NOTE: For this project, we will assume that the glass is uniform in thickness for the sides and bottom.We acknowledge that the rocks and plants take up space in the aquarium, but will assume for this projectthat the 70-gallon volume is measured without any objects in the tank and there would not be an air spacebetween the water and the top. From the picture, we know there will be a black base, which will make thetable higher, but this doesn't affect the computations for the tank. 1Optimization Ftoject70 gallons:9.338 cubicfeetTable TopメA-ち.655 -4.289Cubic feetX+4=レ65S→ h=9.35る9.358= x2hh=D9.358=1.328 cubic feetA-x+リメh:メ+4x19.358(2-605)A"=2+d(32צ.ר3x2X2= x?+ 37.432(会こ2-37.432 4_ (x)= 2-37.432(-(x=) ))=2-37.4る21-A =2x+ 37.432x-2こZx-37.4322x- 2x-37.432= 2- 37.432 (-x (2x))= 2-37.432 (-2x" (x)= 2-37.432 2x):2-37.432 (-2x)O=2x-37.432ZX = - 37,432= Z+ 74.864 (x)Zx3= -37.432=2+74.864=2+74.864x3 =X= 318.714こ18.716×るX= 2.655 cubicfeet

Since you have sent multiple parts so according to our policies we can just send solution of any 3 parts. However i am providing you with solution of the dimensions of the table and also how i got to it. Hope you like it and if you want solution to rest of the parts you can resend the question mentioning the parts of which you want the answer for.

Math

Advanced Math

The table aquarium shown above holds 70 gallons of water. The tank has a square base and the top extends 4 inches past each side. Suppose the amount of glass used to build the aquarium tank is optimized, how nuch glass was needed to build this aquarium? What are the dimensions of the tank? What are the dimensions of the tabletop? Your group is to write a report that explains your findings. The report must include the following: • Submit one project/report per group. Be sure to include everyone's names, first and last. • Restate each question and clearly explain how you found the solution. 1st and 2nd derivative tests to solve the problem and justify your work. • Graphs of the 1* and 2nd derivatives with important points labeled. Concluding paragraph.

The table aquarium shown above holds 70 gallons of water. The tank has a square base and the top extends 4 inches past each side. Suppose the amount of glass used to build the aquarium tank is optimized, how nuch glass was needed to build this aquarium? What are the dimensions of the tank? What are the dimensions of the tabletop? Your group is to write a report that explains your findings. The report must include the following: • Submit one project/report per group. Be sure to include everyone's names, first and last. • Restate each question and clearly explain how you found the solution. 1st and 2nd derivative tests to solve the problem and justify your work. • Graphs of the 1* and 2nd derivatives with important points labeled. Concluding paragraph.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

I need help figuring out the dimensions of the table top. I attached the problem as well as the work I have done

The table aquarium shown above holds 70 gallons of water. The tank has a square base and the top extends
4 inches past each side. Suppose the amount of glass used to build the aquarium tank is optimized, how
much glass was needed to build this aquarium? What are the dimensions of the tank? What are the
dimensions of the tabletop?
Your group is to write a report that explains your findings. The report must include the following:
• Submit one project/report per group. Be sure to include everyone's names, first and last.
• Restate each question and clearly explain how you found the solution.
1st and 2nd derivative tests to solve the problem and justify your work.
• Graphs of the 1 and 2nd derivatives with important points labeled.
Concluding paragraph.
NOTE: For this project, we will assume that the glass is uniform in thickness for the sides and bottom.
We acknowledge that the rocks and plants take up space in the aquarium, but will assume for this project
that the 70-gallon volume is measured without any objects in the tank and there would not be an air space
between the water and the top. From the picture, we know there will be a black base, which will make the
table higher, but this doesn't affect the computations for the tank.

1Optimization Ftoject
70 gallons:
9.338 cubic
feet
Table Top
メ
A-ち.655 -4.289
Cubic feet
X+4=レ65S
→ h=9.35る
9.358= x2h
h=D9.358
=1.328 cubic feet
A-x+リメh
:メ+4x19.358
(2-605)
A"=2+d
(32צ.ר3
x2
X2
= x?+ 37.432
(会
こ2-37.432 4_ (x)
= 2-37.432(-(x=) ))
=2-37.4る2
1-
A =2x+ 37.432x
-2
こZx-37.4322x
- 2x-37.432
= 2- 37.432 (-x (2x))
= 2-37.432 (-2x" (x)
= 2-37.432 2x)
:2-37.432 (-2x)
O=2x-37.432
ZX = - 37,432
= Z+ 74.864 (x)
Zx3= -37.432
=2+74.864
=2+74.864
x3 =
X= 318.714
こ18.716
×る
X= 2.655 cubic
feet

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