Pls Help me Pls

Question

A courier service company has contracted you to design a closed cardboard box with a square base with sides of length x cm, height of length h cm and volume 1000cm³

(a) Write an expression for the volume of this box in terms of x and h.

 

(b) Express the height h, as a function of x.

(c) Show that the surface area A, written as a function of x is given by A(x) = 2x² +4000/x

.
(d) Write down the equation of the vertical asymptote of the graph of A(x).

 

(e) What is a reasonable domain for A(x)? Explain.

 

 

(f) Why might the courier service be interested in designing a box that minimises the surface area?

 

(g) The minimum possible surface area for the box is 600 cm². Find the dimensions of the box with this surface area.

Answer 1

a) V=h*x²  1000=h*x²

 

 

b)h=1000/x²

 

c) surface area=2x²+4*x*h

 

substitute h=1000/x²

 

A= 2x² +4000/x

 

d) x=0 i.e. y axis

 

e) x>0

 

f) To minimize the packing expenses.

 

g) 600= 2x² +4000/x

 

simplifying

 

2x³ -600x+4000=0

 

By solving this equation we get

 

x={10 ,-20}

 

x= 10 only ignore negative answer -20

 

h=1000/100=10