Answer:
Step-by-step explanation:
Represent the volume of the box with V and the dimensions with l, b and h.
The volume (V) is:
Make h the subject of the formula
The surface area (S) of the aquarium is:
Where lb represents the area of the base (i.e. slate):
The cost (C) of the surface area is:
Substitute for h in the above equation
Differentiate with respect to l and with respect to b
To solve for b and l, we equate both equations and set l to b (to minimize the cost)
By comparison:
becomes
Cross Multiply
Solve for l
Recall that:
Also recall that:
Apply law of indices
The dimension that minimizes the cost of material of the aquarium is:
32. y^3-5y^2=0
y^2(y-5)=0
y=0,5
33. 18s^3=50s
18s^2=50
s=+\-sqrt(25/9)=5/3,-5/3
36. 4w^4+40w^2-44=0
4(w^4+10w^2-11)=0
(w^2+11)(w^2-1)=0
w=0,1,+\-sqrt(11)
37. 4z^5=84z^3
4z^2=84
z=+\-sqrt(21)
40. 48p^5=27p^3
48p^2=27
p=+\-sqrt(27/48)=+\-sqrt(9/16)=3/4,-3/4
Any question please feel free to ask. Thanks
Answer: 28.5 pages a day
Step-by-step explanation:
hope it helps!