Answer:
Um, there is nothing here, what's the image of the composite solid?
Answer:
-10
Step-by-step explanation:
Let´s evaluate the complex number:
![4*(\frac{3}{2} -\frac{1}{2}i)^{2} -12*(\frac{3}{2} -\frac{1}{2}i)](https://tex.z-dn.net/?f=4%2A%28%5Cfrac%7B3%7D%7B2%7D%20-%5Cfrac%7B1%7D%7B2%7Di%29%5E%7B2%7D%20-12%2A%28%5Cfrac%7B3%7D%7B2%7D%20-%5Cfrac%7B1%7D%7B2%7Di%29)
First let's calculate this expression:
![(\frac{3}{2} -\frac{1}{2}i)^{2} =(\frac{3}{2} -\frac{1}{2}i)*(\frac{3}{2} -\frac{1}{2}i)](https://tex.z-dn.net/?f=%28%5Cfrac%7B3%7D%7B2%7D%20-%5Cfrac%7B1%7D%7B2%7Di%29%5E%7B2%7D%20%3D%28%5Cfrac%7B3%7D%7B2%7D%20-%5Cfrac%7B1%7D%7B2%7Di%29%2A%28%5Cfrac%7B3%7D%7B2%7D%20-%5Cfrac%7B1%7D%7B2%7Di%29)
Using distributive property:
![(\frac{3}{2} )^{2} -2*(\frac{3}{2}*\frac{1}{2}i )+(\frac{1}{2}i )^{2}](https://tex.z-dn.net/?f=%28%5Cfrac%7B3%7D%7B2%7D%20%29%5E%7B2%7D%20-2%2A%28%5Cfrac%7B3%7D%7B2%7D%2A%5Cfrac%7B1%7D%7B2%7Di%20%29%2B%28%5Cfrac%7B1%7D%7B2%7Di%20%29%5E%7B2%7D)
Where:
![i=\sqrt{-1}](https://tex.z-dn.net/?f=i%3D%5Csqrt%7B-1%7D)
Therefore:
![2-\frac{3}{2} i](https://tex.z-dn.net/?f=2-%5Cfrac%7B3%7D%7B2%7D%20i)
Evaluating the rest of the expression using the distributive property again:
![4*(2-\frac{3}{2} i)-12*(\frac{3}{2} -\frac{1}{2}i)=8-6i-18+6i=-10](https://tex.z-dn.net/?f=4%2A%282-%5Cfrac%7B3%7D%7B2%7D%20i%29-12%2A%28%5Cfrac%7B3%7D%7B2%7D%20-%5Cfrac%7B1%7D%7B2%7Di%29%3D8-6i-18%2B6i%3D-10)
Answer:
part 1: slope of AB : 3
equation of line p: y = 3x -10
Step-by-step explanation:
part 1: slope of AB = (4-1) / (2-1) = 3
part 2: y = mx + b
b = 2 - (3 × 4) = -10
equation: y = 3x -10
Y= 2x + 3 because it’s wanting it to be the total cost.
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