Answer for the first one is just 7/9, 28/36
Second one is 9/14, 3/4
For the third one you multiply 12.50 by 5 which gives you 62.5
To tell whether r = 2 is a solution of the inequality, substitute 2 for r and see whether the inequality produces a true or a false statement.
(2) + 4 > 8, add 2 and 4.
6 > 8, this is a false statement, because 6 is not greater than 8, so the value r = 2 is not a solution of the inequality r + 4 > 8.
Answer:
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).
![n\geq \frac{log(\frac{b-a}{\epsilon} )}{log(2)}](https://tex.z-dn.net/?f=n%5Cgeq%20%5Cfrac%7Blog%28%5Cfrac%7Bb-a%7D%7B%5Cepsilon%7D%20%29%7D%7Blog%282%29%7D)
We know
a = -2, b = 1 and ε =
so
![n\geq \frac{log(\frac{1+2}{10^{-8}} )}{log(2)}\\n \geq 29](https://tex.z-dn.net/?f=n%5Cgeq%20%5Cfrac%7Blog%28%5Cfrac%7B1%2B2%7D%7B10%5E%7B-8%7D%7D%20%29%7D%7Blog%282%29%7D%5C%5Cn%20%5Cgeq%2029)
Thus, n = 29 iterations would be enough to obtain a root of
that is at most
away from the correct solution.
<u>You can prove this result by doing the computation as follows:</u>
From the information given we know:
This is the algorithm for the Bisection method:
- Find two numbers <em>a</em> and <em>b</em> at which <em>f</em> has different signs.
- Define
![c=\frac{a+b}{2}](https://tex.z-dn.net/?f=c%3D%5Cfrac%7Ba%2Bb%7D%7B2%7D)
- If
then accept c as the root and stop - If
then set <em>c </em>as the new<em> b</em>. Otherwise, set <em>c </em>as the new <em>a</em>. Return to step 1.
We know that
and
so we take
and
then ![c=\frac{-2+1}{2} =-0.5](https://tex.z-dn.net/?f=c%3D%5Cfrac%7B-2%2B1%7D%7B2%7D%20%3D-0.5)
Because
we set
as the new <em>b.</em>
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
Answer:
b
Step-by-step explanation:
-a-(a-b)
Distribute the negative sign to get -a+a+b
-a cancels out a, and you're left with b.
Answer:
Step-by-step explanation:
First write out the vector and do the computation.
After that sketch the vector on the graph the arrow show where the vector is pointing to.
You can use the vector v to find the unit vector