Find the minimum number of iterations needed by the bisection method to approximate the root of the function f( x)= x^ 3-6x^ 2+11x-6 between ( 2.5,4) with error tolerance 10^ -3​

hello :

by applying the distributive property :

6 × 4.3 = 6 × ( 4 + 0.3 )

            =   (6 ×   4) + (6 ×   0.3)

            = 24 + 1.8

6 × 4.3 = 25.8

step-by-step explanation:

consider an orange peel: if you want to try and lay it flat, you have to stretch it, we know exactly how things are being stretched or squashed at any given point. we have many different map projections because each has different patterns of some projections can even preserve certain features of the earth without

x= 1

step-by-step explanation: convert 5\frac{11}{12}5

​12

​

​11

​​   to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

​c

​

​b

​​ =

​c

​

​ac+b

​​

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{5\times 12+11}{12}3.25+0.5x+1

​3

​

​1

​​ +

​6

​​5

​​ x=

​12

​5×12+11

​​ 2 simplify 5\times 125×12 to 6060

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{60+11}{12}3.25+0.5x+1

​3

​​1

​​ +

​6

​5

​​ x=

​12

​​60+11

​​3 simplify 60+1160+11 to 7171

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{71}{12}3.25+0.5x+1

​3

​​1

​​ +

​6

​​5

​​ x=

​12

​​71

​​4 simplify \frac{5}{6}x

​6

​​5

​​ x to \frac{5x}{6}

​6

​5x

​​ 3.25+0.5x+1\frac{1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+1

​3

​

​1

​​ +

​6

​5x

​​ =

​12

​​71

​​ 5 convert 1\frac{1}{3}1

​3

​​1

​​   to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

​c

​​b

​​ =

​c

​​ac+b

​​3.25+0.5x+\frac{1\times 3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

​3

​​1×3+1

​​ +

​6

​​5x

​​ =

​12

​71

​​ 6 simplify 1\times 31×3 to 33

3.25+0.5x+\frac{3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

​3

​​3+1

​​ +

​6

​​5x

​​ =

​12

​71

​​ 7 simplify 3+13+1 to 44

3.25+0.5x+\frac{4}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

​3

​​4

​​ +

​6

​5x

​​ =

​12

​71

​​8 simplify 3.25+0.5x+\frac{4}{3}+\frac{5x}{6}3.25+0.5x+

​3

​​4

​​ +

​6

​​5x

​​   to \frac{13.75}{3}+\frac{4x}{3}

​3

​​13.75

​​ +

​3

​4x

​​ \frac{13.75}{3}+\frac{4x}{3}=\frac{71}{12}

​3

​​13.75

​​ +

​3

​​4x

​​ =

​12

​71

​​ 9 simplify \frac{13.75}{3}

​3

​​13.75

​​   to 4.5833334.583333

4.583333+\frac{4x}{3}=\frac{71}{12}4.583333+

​3

​​4x

​​ =

​12

​71

​​ 10 subtract 4.5833334.583333 from both sides

\frac{4x}{3}=\frac{71}{12}-4.583333

​3

​

​4x

​​ =

​12

​

​71

​​ −4.583333

11 simplify \frac{71}{12}-4.583333

​12

​

​71

​​ −4.583333 to \frac{4}{3}

​3

​4

​\frac{4x}{3}=\frac{4}{3}

​3

​​4x

​​ =

​3

​4

​​ 12 multiply both sides by 33

4x=\frac{4}{3}\times 34x=

​3

​4

​​ ×3

13 simplify \frac{4}{3}\times 3

​3

​​4

​​ ×3 to \frac{12}{3}

​3

​​12

​​ 4x=\frac{12}{3}4x=

​3

​​12

​​ 14 simplify \frac{12}{3}

​3

​​12

​​   to 44

4x=44x=4

15 divide both sides by 44

x=1

​​

answer: answer is b.

[m < b = 120º]

step-by-step explanation: