I hope this helps. Good luck, I was in the same boat not too long ago.
1) given ,
4x-24=1000
=> 4x = 1000+24
=> 4x = 1024
=> x = 256
2)Given , 7x= 343
=> x = 343/7
=> x = 49
3) given , x^4 = 4096
=> x = fourth root of 4096
=> x = 8
Answer:
The base and height of the solid is 5.5cm
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Step-by-step explanation:
Given

Required
Determine the dimensions that maximizes the volume
Let the base dimension be x and the height be h
The volume is calculated as:


181.5 =x^2h
The surface area (S) is calculated as this:



Substitute 181.5 for S

Make h the subject:


Substitute
in 





To get the maximum, we differentiate V with respect to t and set the differentiation to 0

Set to 0


Multiply through by 4







Recall that:





So, we have:


<em>Hence, the base and height of the solid is 5.5cm</em>