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kati45 [8]
3 years ago
10

Solve in C: (3+2i)z+1-2i=2iz-2+i

Mathematics
1 answer:
stellarik [79]3 years ago
5 0
Hello,
(3+2i)z+1-2i=2iz-2+i
<==>(3+2i-2i)z=-2+i-1+2i
<==>3z=3(-1+i)
<==>z=-1+i

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The population of a local species of bees can be found using an infinite geometric series where a1=860 and the common ratio is 1
erma4kov [3.2K]
a_1=860
a_2=\dfrac{a_1}5
a_3=\dfrac{a_2}5=\dfrac{a_1}{5^2}
\vdots
a_n=\dfrac{a_{n-1}}5=\dfrac{a_{n-2}}{5^2}=\cdots=\dfrac{a_1}{5^{n-1}}

The kth partial sum is

\displaystyle S_k=\sum_{n=1}^ka_n=\sum_{n=1}^k\frac{a_1}{5^{n-1}}
S_k=a_1\left(1+\dfrac15+\dfrac1{5^2}+\cdots+\dfrac1{5^{k-2}}+\dfrac1{5^{k-1}}
\dfrac15S_k=a_1\left(\dfrac15+\dfrac1{5^2}+\dfrac1{5^3}+\cdots+\dfrac1{5^{k-1}}+\dfrac1{5^k}\right)

\implies S_k-\dfrac15S_k=a_1\left(1-\dfrac1{5^k}\right)
\dfrac45 S_k=860\left(1-\dfrac1{5^k}\right)
S_k=1075-\dfrac{1075}{5^k}

As k\to\infty, we're left with

\displaystyle\sum_{n=1}^\infty a_n=\lim_{k\to\infty}\left(1075-\frac{1075}{5^k}\right)=1075

which is the upper limit to the population of the bees.
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3 years ago
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What is the graph of the function rule? Y=|5x|-2
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<span>y = 5x – 2  y = 5(11) – 2  y = 55 – 2 = 49
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aleksandrvk [35]

Answer:

A conditional statement is something like:

If P, then Q.

P = hypothesis.

Q = conclusion.

In this case, we have:

"If a polygon is a quadrilateral, then it is a square".

1) The hypothesis is: a polygon is a quadrilateral

2) The conclusion is:  it is a square

3) It is not true, because there are other quadrilaterals that are not squares, for example, the rectangles.

4) The inverse of a conditional statement is (using the same notation than above)

If not P, then not Q.

In this case is:

"If a polygon is not a quadrilateral, then it is not a square"

(this is true)

5) A converse statement is:

If Q, then P

In this case is:

"if it is a square, then the polygon is a quadrilateral"

(Also true)

6) A biconditional statement is written as:

P if and only if Q.

In this case is:

A polygon is a quadrilateral if and only if it is a square.

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