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3 years ago

Which of the following is the rule for rotating the point with coordinates (x,y), 180° counterclockwise about the origin?

Mathematics

2 answers:

amm18123 years ago

6 0

Answer:

D. (x, y) → (-x, -y)

Step-by-step explanation:

A. (x,y) → (y,x) . . . . reflects across the line y=x

B. (x,y) → (y,-x) . . . . rotates 90° CCW

C. (x,y) → (-y,-x) . . . . reflects across the line y=-x

D. (x,y) → (-x,-y) . . . . rotates 180° about the origin

ohaa [14]3 years ago

4 0

Answer:

The correct option is D.

Step-by-step explanation:

If a point rotating 180° counterclockwise about the origin, then the sign of each coordinate is changed.

Consider the coordinates of a point are (x,y).

If a (x,y) rotating 180° counterclockwise about the origin, then the rule of rotation is defined as

$(x,y)\rightarrow (-x,-y)$

In which (x,y) is the coordinate pair of preimage and (-x,-y) is the coordinate pair of image.

Therefore the correct option is D.

If a point reflects across the line y=x , then

$(x,y)\rightarrow (y,x)$

If a point rotated 90° clockwise, then

$(x,y)\rightarrow (y,-x)$

If a point reflects across the line y=-x, then

$(x,y)\rightarrow (-y,-x)$

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IRINA_888 [86]

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3 years ago

Read 2 more answers

Evaluate the expression: v ? w Given the vectors: r = <8, 1, -6>; v = <6, 7, -3>; w = <-7, 5, 2> . If the answ

Snezhnost [94]

Answer:

-13

Step-by-step explanation:

Given are two vectors v and w.

v=(6,7,-3) and

w=(-7,5,2)

We are to find the dot product of v.w

We have

Dot product is obtained by multiplying corresponding pairs and adding them

Here we have

v.w=6(-7)+7(5)-3(2)

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7 0

3 years ago

WHAT IS THE ANSWER FOR 12 1/3 + 8 3/4 +17 2/8 +23 2/3=

gulaghasi [49]

$12 \dfrac{1}{3} + 8 \dfrac{3}{4} +17 \dfrac{2}{8} +23 \dfrac{2}{3}$

Simplify
$= 12 \dfrac{1}{3} + 8 \dfrac{3}{4} +17 \dfrac{1}{4} +23 \dfrac{2}{3}$

Change the denominators to be the same
$= 12 \dfrac{1 \times 4}{3 \times 4} + 8 \dfrac{3 \times 3}{4 \times 3} +17 \dfrac{1 \times 3 }{4 \times 3} +23 \dfrac{2 \times 4}{3 \times 4}$

$= 12 \dfrac{4}{12} + 8 \dfrac{9}{12} +17 \dfrac{3 }{12} +23 \dfrac{8}{12}$

Combine into single fraction
$= 60 \dfrac{24}{12}$

$= 62$

6 0

2 years ago

Use any of the methods to determine whether the series converges or diverges. Give reasons for your answer.

Aleks [24]

Answer:

It means $\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}$ also converges.

Step-by-step explanation:

The actual Series is::

$\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}$

The method we are going to use is comparison method:

According to comparison method, we have:

$\sum_{n=1}^{inf}a_n\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n$

If series one converges, the second converges and if second diverges series, one diverges

Now Simplify the given series:

Taking"n^2"common from numerator and "n^6"from denominator.

$=\frac{n^2[7-\frac{4}{n}+\frac{3}{n^2}]}{n^6[\frac{12}{n^6}+2]} \\\\=\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{n^4[\frac{12}{n^6}+2]}$

$\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n=\sum_{n=1}^{inf} \frac{1}{n^4}$

Now:

$\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\ \\\lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\=\frac{7-\frac{4}{inf}+\frac{3}{inf}}{\frac{12}{inf}+2}\\\\=\frac{7}{2}$