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Lena [83]
3 years ago
15

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.
5 0
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

8 0
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.

The average rate of change can be calculated using formula

\dfrac{f(b)-f(a)}{b-a}

In your case,

a=10\\ \\b=20,

then

f(a)=-10^2+20\cdot 10+100=-100+200+100=200\\ \\f(b)=-20^2+20\cdot 20+100=-400+400+100=100

and the average rate of change is

\dfrac{100-200}{20-10}=\dfrac{-100}{10}=-10

This means the crop yield decreased by 10 pounds per acre (negative rate of change) from year 10 to year 20.

5 0
3 years ago
Read 2 more answers
How many terms are there in the following expression: 3a + 3ab + 7b – 2c – 4d?
AfilCa [17]
The correct answer is that there are  5 terms in this problem

3 0
3 years ago
Solve using the quadratic equation.
castortr0y [4]

Answer:

X = 4

X = -2

Step-by-step explanation:

Rate And Like. Salute.

4 0
2 years ago
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