Here is another one that i need help with

Mathematics

2 answers:

Virty [35]3 years ago

7 0

The first one is the answers

solong [7]3 years ago

6 0

Translation
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Swimmer on 4x100 relay team each swim 100 meter, and their individual times are totaled to form their overall team time. A parti

vovikov84 [41]

Answer:

250 secs

Step-by-step explanation:

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3 years ago

Whats the next number in this pattern 2,3,5,9,17

umka21 [38]

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Hope that helps! Have a good day :)

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3 years ago

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]

Lady_Fox [76]

Answer:

n = 29 iterations would be enough to obtain a root of $f(x)=2x^2-3x-2$ that is at most $10^{-8}$ 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).

$n\geq \frac{log(\frac{b-a}{\epsilon} )}{log(2)}$

We know

a = -2, b = 1 and ε = $10^{-8}$ so

$n\geq \frac{log(\frac{1+2}{10^{-8}} )}{log(2)}\\n \geq 29$

Thus, n = 29 iterations would be enough to obtain a root of $f(x)=2x^2-3x-2$ that is at most $10^{-8}$ away from the correct solution.

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

From the information given we know:

$f(x)=2x^2-3x-2$
$\epsilon = 10^{-8}$

This is the algorithm for the Bisection method:

Find two numbers a and b at which f has different signs.
Define $c=\frac{a+b}{2}$
If $b-c\leq \epsilon$ then accept c as the root and stop
If $f(a)f(c)\leq 0$ then set c as the new b. Otherwise, set c as the new a. Return to step 1.