Mathematics, 08.10.2019 11:20 michellestepp2001

Circle
p
has center
p
(2, 0) and radius 20. circle
q
has center
q
(0, 4) and radius 2.
(a)
describe the rule for translating center
q
onto center
p
.
(b)
determine the scale factor for dilating circle
q
so that it has the same radius as circle
p.
(c)
are circles
p
and
q
similar? explain your answer.

Answers: 1

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Answers

Answer from: kenoknox

Siras ! Don't try to picture this all in your head !
You'll wear out your brain.
You MUST sketch it on a piece of paper.
Draw an x-axis and a y-axis, then draw the two circles.

I'm drawing myself a picture right now, and I'm
supposed to be some kind of a genius.

a). In order to move Circle-Q so that both centers are
at the same point, you need to move the center of Q
4 units down and 2 units to the right.
      When you do that, you'll have the little circle inside the
big circle, with their centers both at the same place.

b). The radius of Q is 2.
   The radius of P is 20.
   What do you have to multiply 2 by, in order to get 20 ?
   THAT's the scale factor to dilate Q so that it has the same
radius as P.
   When you do that, suddenly it'll look like you only have one circle
on the paper ... they'll both have the same radius and their centers are
at the same place, so you can't tell them apart.

c). All circles are similar !

I went online (you could easily go there too). I searched the question
"Are circles similar ?" and a lot of interesting stuff came up. (you could
do that too). I saw a lot of ways to prove that all circles are similar.
The best one says:

   Two figures are "similar" if you can make one of them
   exactly fit on top of the other one (make them congruent)
   with translations and dilations.

You just did that with P and Q !

-- Translation is moving them around.
   You moved Q and put the centers of both circles at the same place.

-- Dilation is blowing it up or blowing it down, so its size changes
but its shape doesn't change.
   You blew Q up so that it had the same radius as P.
   Then the two circles exactly fit over/under each other.

So the two circles are similar.

Answer from: Quest

about 5.6 days

step-by-step explanation:

we can fill the given information into the decay equation and solve for the value of t at which half the sample remains.

$\dfrac{11}{2} =11e^{-0.1247t} \qquad\text{decay equation with values filled in}\\\\\dfrac{1}{2}=e^{-0.1247t} \qquad\text{divide by 11}\\\\-\ln{(2)}=-0.1247t \qquad\text{take the natural log}\\\\\dfrac{\ln{(2)}}{0.1247}=t\approx 5.559\approx 5.6\qquad\text{divide by -0.1247}$

the half-life is about 5.6 days.

Answer from: Quest

2nd one in the first row is correct

Me on this i’m so tired and i can’t sleep until my progress is at 80 and this is the end of my year

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Circle
p
has center
p
(2, 0) and radius 20. circle
q
has cent...