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stich3 [128]
3 years ago
12

2. Describe how to use the conjugate to divide 2 − i by 3 + 2i, and then find the quotient.

Mathematics
1 answer:
DaniilM [7]3 years ago
7 0

Answer:

\frac{4}{13}-\frac{7}{13}i

Step-by-step explanation:

\frac{2-i}{3+2i}

Multiply and divide by the conjugate.

The conjugate is the denominator with the sign of the complex number the opposite of the denominator.

\frac{2-i}{3+2i}\frac{3-2i}{3-2i}\\ =\frac{2\times (3-2i)-i\times (3-2i)}{3^2-(2i)^2}\\ =\frac{6-4i-3i+2i^2}{9+4}\\ =\frac{4-7i}{13}\\ =\frac{4}{13}-\frac{7}{13}i

Quotient = \frac{4}{13}-\frac{7}{13}i

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Can anyone help me solve this
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a. $45.54; b. $51.42; c. See below

Step-by-step explanation:

a. 193 min

        Service charge = $40.00

1st 100 min @ 0.021 =      2.10

Next 93 min @0.037 = <u>    3.44 </u>

                        Total =  $45.54

b. 317 min

          Service charge = $40.00

  1st 100 min @ 0.021 =      2.10

2nd 100 min @ 0.037 =     3.70

        117 min @ 0.048 =   <u>   5.62</u>

                          Total =   $51.42

c. Piecewise function

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which we can write like this:

f(t) =\begin{cases}40.00 + 0.021t & t \leq 100\\42.10 + 0.037(t-100) & 100 < t \leq200\\45.80 + 0.048(t-200) & t > 200\end{cases}

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