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1 year ago

11

N(-2,-2) after a 90 degree counterclockwise rotation

1 answer:

Novay_Z [31]1 year ago

5 0

Answer: (2,-2)

Step-by-step explanation:

Rotating 90 degrees counterclockwise (about the origin) maps (x,y) onto (-y,x), so the answer is <u>N'(2,-2)</u>

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Let f be the function defined as follows:

katen-ka-za [31]

With $f$ defined by

$f(x)=\begin{cases}|x-1|+2&\text{for }x$

in order for it to be continuous at $x=c$ , we require

$\displaystyle\lim_{x\to c^-}f(x)=\lim_{x\to c^+}f(x)=f(c)$

(i) If $a=2$ and $b=3$ , then $f(1)=2(1)^2+3(1)=5$ and

$\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1}|x-1|+2=2$

$\displaystyle\lim_{x\to1^+}f(x)=\lim_{x\to1}2x^2+3x=5$

The limits don't match, so $f$ is not continuous at $x=1$ under these conditions.

(ii) To establish continuity at $x=1$ , we'd need the limit as $x\to1$ from the right to be equal to the limit from the left, or

$\displaystyle\lim_{x\to1}ax^2+bx=\lim_{x\to1}|x-1|+2\iff a+b=2$

(iii) We have $f(2)=0$ and

$\displaystyle\lim_{x\to2^-}f(x)=\lim_{x\to2}ax^2+bx=4a+2b$

$\displaystyle\lim_{x\to2^+}f(x)=\lim_{x\to2}5x-10=0$

For $f$ to be continuous at $x=2$ , then, we'd need to have

$4a+2b=0$

(iv) Taking both requirements from parts (ii) and (iii), we solve for $a,b$ :

$\begin{cases}a+b=2\\4a+2b=0\end{cases}\implies a=-2,b=4$

I've attached a plot that confirms this is correct.

7 0

3 years ago

Evaluate A = bh, for b = 8 and h = 4

pantera1 [17]

Step-by-step explanation:

Well First you Need to Fill it in:

A=bh, b=8 h=4

A=8•4

then you multiply:

8•4=32

Therefore your answer is 32.

Hope this helps! :)

4 0

3 years ago

Monica went shopping for holiday presents. She bought boxes of chocolates and boxes of ornaments for her

Mrrafil [7]

She can buy 6 boxes of chocolates
and 8 boxes of ornaments
6*10=60 & 8*12=96
so you would add them and get
60+96=156

6 0

3 years ago

aleksandrvk [35]

Part a: 1,3,5,7

part b: i’m not sure

5 0

1 year ago

10 to the seventh power

never [62]

10000000 is the answer by multiplication

4 0

3 years ago