An open metal tank of square base has a volume of 157 m3 Given that the square base has sides of length xx metres, find expressions, in terms of xx, for the following. a) Describe the height of the tank in terms of x h= b) Describe the surface area of the tank in terms of x S= c) Find the first derivative S′(x)= and given that the surface area is a minimum, find the value of xx. Therefore, x= (give your answer to 2 decimal places) Find the second derivative S′′(x)= Check this is a minimum. Substitute your value for xx into S″(x) and determine whether is it a minimum. Type 'Y' for yes, 'N' for no, or 'U' for undefined. Hence, calculate the minimum area of metal used Amin= (give your answer to 2 decimal places)
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
An open metal tank of square base has a volume of 157 m3
Given that the square base has sides of length xx metres, find expressions, in terms of xx, for the following.
a)
Describe the height of the tank in terms of x
h=
b)
Describe the surface area of the tank in terms of x
S=
c)
Find the first derivative
S′(x)=
and given that the surface area is a minimum, find the value of xx. Therefore,
x= (give your answer to 2 decimal places)
Find the second derivative
S′′(x)=
Check this is a minimum.
Substitute your value for xx into S″(x) and determine whether is it a minimum.
Type 'Y' for yes, 'N' for no, or 'U' for undefined.
Hence, calculate the minimum area of metal used
Amin= (give your answer to 2 decimal places)
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
