Math Questions

Question

1.) An open box is to be made from a flat piece of material 10 inches long and 5 inches wide by cutting equal squares of length x from the corners and folding up the sides.
Write the volume Vof the box as a function of x. Leave it as a product of factors, do not multiply out the factors.

V=

If we write the domain of the box as an open interval in the form (a,b), then what is a?

a=

and what is b?

b= 

 

 

 

2.) Suppose that x=ln(A) and y=ln(B). Write the following expressions in terms of x and y (so you cannot have an A or B anywhere in your answers). 

 

ln(AB)=

 

 

AB=

 

 

 

 

3.)The following equation is the general form of a circle

2x²+x+2y²−10=0

 

Complete the square to write the equation of the given circle in standard form

(x−h)²+(y−k)²=r²

 

to determine the center (h,k) and the radius r.


h=


k=


r=

Answer 1

V = (5-2x)(10-2x) = 4x^2 -30x + 50