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The function of x has two separate x terms multiplied by each other. Therefore, the appropriate way to integrate this function is by parts. The equation for integration by parts is [integral (u.dv/dx)] = ...

We can turn this into a constrained optimization problem. Let's denote x the side of the parking lot that is perpendicular to the highway, and y the side that is parallel to the highway. We therefore need...

2x become x²

3x^1/2 becomes 2x^3/2

1 becomes x

sub 9 into values for x = (81 - 54 +9) which equals 36

sub 4 into values for x = (16 - 16 + 4) whi...

9^ (3x + 1)

We know that 3 to power of 2 equals 9.  3x3 = 3^2 = 9, 

= 3^ (2 * [3x + 1])

We simply the term because 2 * [3x + 1] = 6x + 2

= 3^ ( 6x + 2) 

This term is in ...

Firstly, solve 0=14-x^2 to find the horisontal distance to the edges of the tunnel. x1=sqrt(14), x2= -sqrt(14).

Integrate h=14-x^2 between x1 and x2 28*sqrt(14) -(2(sqrt(14)^3))/3. This is the requ...