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DerKrebs [107]
1 year ago
11

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

Mathematics
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
Part A
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
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