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Artyom0805 [142]
3 years ago
14

Divide the following complex numbers: (6-i)/(5+4i)

Mathematics
1 answer:
katen-ka-za [31]3 years ago
6 0
(6-i)/(5+4i)=
Multiply both numerator and denominator by (5-4i):
(6-i)(5-4i)/(5+4i)(5-4i)=
(30-24i-5i+4i^2)/(5^2-16i^2)=
(30-29i+4i^2)/(25-16i^2)=
i^2 = -1
(30-29i+4×(-1))/(25-16×(-1))=
(26-29i)/41
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sergejj [24]

Answer:

Ben's rate is \dfrac{1}{6} greater than Kate's rate.

Step-by-step explanation:

1. If it takes Ben 2 days to write reports, then his rate is \dfrac{1}{2} of reports per day.

2. If it takes Kate 3 days to write reports, then her rate is \dfrac{1}{3} of reports per day.

3. Ben's rate is

\dfrac{1}{2}-\dfrac{1}{3}=\dfrac{3-2}{6}=\dfrac{1}{6}

greater than Kate's rate.

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4 years ago
Option 1:<br><br> Find x. Show all work.
Ronch [10]

Using law of cosines:

Cos(angle) = adjacent/ hypotenuse


Cos(22) = 12/x

Rewrite to get:

X = 12/cos(22)

Simplify:

X = 12.9424

Round the answer as needed.

5 0
3 years ago
Read 2 more answers
X+1<br> -<br> and h(x) = 4 - X, what is the value<br> Oil CD<br> Nior<br> wla<br> olo
timofeeve [1]

Answer:

8/5

Step-by-step explanation:

(g\circ h)(-3) means g(h(-3)).

Start with the inside first: h(-3).

h(-3) means use the function called h and replace the x with -3.  The expression that is called h is 4-x.

4-x evaluated at x=-3 gives us 4-(-3)=4+3=7.

So the value for h(-3) is 7, or h(-3)=7.

Now this is what we thus far:

(g\circ h)(-3)=g(h(-3))=g(7).

g(7) means use the function called g and replace x with 7.   The expression that is called g is (x+1)/(x-2).

(x+1)/(x-2) evaluated at x=7 gives us (7+1)/(7-2)=(8)/(5)=8/5.

This is our final answer:

(g\circ h)(-3)=g(h(-3))=g(7)=\frac{8}{5}.

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3 years ago
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3 years ago
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Amar keeps picking playing cards out of a standard deck of 52 cards in the hopes that he will
lapo4ka [179]

Answer:

The required probability is, 0.78

Step-by-step explanation:

There are, (52 - 13) = 39 cards which are not spade

5 cards can be chosen from the deck of 52 cards in

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and out of these 5 choices, none of them will be spade in,

^{39}{C}_{5}  ways

So,

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Hence,

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4 0
4 years ago
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