Find n for which the nth iteration by the bisection method guarantees to approximate the root of f(x) = 2x^2 − 3x − 2 on [−2, 1] with accuracy within 10^−8 .

n = 29 iterations would be enough to obtain a root of that is at most away from the correct solution.

Step-by-step explanation:

You can use this formula which relates the number of iterations, n, required by the bisection method to converge to within an absolute error tolerance of ε starting from the initial interval (a, b).

We know

a = -2, b = 1 and ε = so

Thus, n = 29 iterations would be enough to obtain a root of that is at most away from the correct solution.

You can prove this result by doing the computation as follows:

From the information given we know:

This is the algorithm for the Bisection method:

We know that and so we take and then

Because we set as the new b.

The bisection algorithm is detailed in the following table.

After the 29 steps we have that hence the required root approximation is c = -0.50

she played for 18.75 hours.

step-by-step explanation:

if she played 2/4 of a hour on tuesday. and there is 60 minutes in an hour and 60 divided by 4 is 7.5. and she played 2/4 of an hour on thursday then again 60 divided by 4 is 7.5, you add 7.5+7.5=56.25. now you have to do 1/4 of an hour, it equals 3.75. now you have to add them all up. 3.75+7.5+7.5=18.75

i hope this and i hope you get it right. it took me a while to get this done for you. : )

answer: 1,380

step-by-step explanation:

1: you turn %15 into a decimal by moving the decimal point two places to the left.

2: and then you multiply .15 by 1,200 , which will get you 180.00

3: from there you will add 180 to 1,200

4: which will get you 1,380

hope it *im kind of slow so idk if my answer is right*