A piece of wire of length 7070 is cut, and the resulting two pieces are formed to make a circle and a square. Where should the wire be cut to (a) minimize and (b) maximize the combined area of the circle and the square?

a.x=39.2

b.Use whole  wire as a circle

Step-by-step explanation:

We are given that

Length of piece of wire=70  units

Let length of wire used to make a square =x units

Length of wire used in circle=70- x

Side of square=

Circumference of circle=

Combined area of circle and square,A=

Using the formula

Area of circle=

Area of square=

a.

Differentiate w.r.t x

x=39.2

Again differentiate w.r.t x

>0

Hence, the combined area of circle and the square is minimum at x=39.2

b.When the wire is not cut and whole wire used  as a circle . Then, combined area is maximum.

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

you bought 31 v bucks

step-by-step explanation:

25+6=31