Find the coordinates of the intersection of the diagonals of the parallelogram with the vertices Q(-1,3), R(5,2), S(1, - 2), and

Mathematics

1 answer:

Vadim26 [7]3 years ago

4 0

Answer:0,0.5

Step-by-step explanation:

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Examine the pattern in the powers of i you wrote in the table, and create a rule for finding the value of large powers of i. Jus

denpristay [2]

Let $N$ be any integer. Then

$i^N=\begin{cases}1&\text{if }N\equiv0\mod4\\i&\text{if }N\equiv1\mod4\\-1&\text{if }N\equiv2\mod4\\-i&\text{if }N\equiv3\mod4\end{cases}$

In other words:

(1) If $N$ is a multiple of 4, then $i^N=1$ .

(2) If dividing $N$ by 4 leaves a remainder of 1, then $i^N=i$ , since $i^N=i^{4n+1}$ for some integer $n$ , and from (1) we know that $i^{4n+1}=i^{4n}i=i$ (because, obviously, $4n$ is a multiple of 4).

(3) If instead you get a remainder of 2, then $i^N=-1$ . This follows from (1) as well. $i^N=i^{4n+2}=i^{4n}i^2=(1)(-1)=-1$ .

(4) Finally, if you get a remainder of 3, then $i^N=i^{4n+3}=i^{4n}i^2i=(1)(-1)(i)=-i$ .

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3 years ago

Maggie is rock climbing. After reaching the summit, she descends at a rate of 7 feet each minute. If she continues at this rate,

Slav-nsk [51]

Answer:

she will have gone down 56 feet

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3 years ago

A farmer is tracking the number of soybeans his land is yielding each year. He finds that the function f(x) = −x2 + 20x + 100 mo

Aliun [14]

Answer:

The average rate of change = -10

The crop yield decreased by 10 pounds per acre from year 10 to year 20.

Step-by-step explanation:

A farmer is tracking the number of soybeans his land is yielding each year. He finds that the function $f(x) =-x^2 + 20x + 100$ models the crops in pounds per acre over x years.