19.01.2023

Given two concentric circles (circles that have the same center point), with the inner circle having a radius of r1 and the outer one having a radius of

r2 as shown, give a dilation that would map the inner circle onto the outer

circle. Specify both the center of dilation and the scale factor.

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09.07.2023, solved by verified expert
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The center of dilation has a coordinate of Given two concentric circles (circles that have, №18009817, 19.01.2023 02:21 and the scale factor is Given two concentric circles (circles that have, №18009817, 19.01.2023 02:21. The transformation formula is Given two concentric circles (circles that have, №18009817, 19.01.2023 02:21.

How to define a dilation between two concentric circles

Two circles are concentric when they share the same center (Given two concentric circles (circles that have, №18009817, 19.01.2023 02:21) but they have different radii (Given two concentric circles (circles that have, №18009817, 19.01.2023 02:21), where Given two concentric circles (circles that have, №18009817, 19.01.2023 02:21 corresponds to the radius of the smaller circle. By analytic geometry we know that circles are modeled after this formula:

Given two concentric circles (circles that have, №18009817, 19.01.2023 02:21     (1)

If we assume that the center of dilation is the center of both circles and the dilation use a scale factor of Given two concentric circles (circles that have, №18009817, 19.01.2023 02:21. Then, we have the following expression:

Given two concentric circles (circles that have, №18009817, 19.01.2023 02:21    

Given two concentric circles (circles that have, №18009817, 19.01.2023 02:21     (2)

The center of dilation has a coordinate of Given two concentric circles (circles that have, №18009817, 19.01.2023 02:21 and the scale factor is Given two concentric circles (circles that have, №18009817, 19.01.2023 02:21. The transformation formula is Given two concentric circles (circles that have, №18009817, 19.01.2023 02:21. Given two concentric circles (circles that have, №18009817, 19.01.2023 02:21

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Mathematics
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P Answered by Specialist

The center of dilation has a coordinate of (x,y) = (h,k) and the scale factor is r. The transformation formula is r^{2} = \frac{(x_{2}-h)^{2}+(y_{2}-k)^{2}}{(x_{1}-h)^{2}+(y_{1}-k)^{2}}.

How to define a dilation between two concentric circles

Two circles are concentric when they share the same center (h, k) but they have different radii (r_{1}, r_{2}), where r_{1} corresponds to the radius of the smaller circle. By analytic geometry we know that circles are modeled after this formula:

(x-h)^{2}+(y-k)^{2} = r^{2}     (1)

If we assume that the center of dilation is the center of both circles and the dilation use a scale factor of r. Then, we have the following expression:

r= \frac{r_{2}}{r_{1}}    

r^{2} = \frac{(x_{2}-h)^{2}+(y_{2}-k)^{2}}{(x_{1}-h)^{2}+(y_{1}-k)^{2}}     (2)

The center of dilation has a coordinate of (x,y) = (h,k) and the scale factor is r. The transformation formula is r^{2} = \frac{(x_{2}-h)^{2}+(y_{2}-k)^{2}}{(x_{1}-h)^{2}+(y_{1}-k)^{2}}. \blacksquare

To learn more on dilations, we kindly invite to check this verified question:

Mathematics
Step-by-step answer
P Answered by PhD

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

Mathematics
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P Answered by PhD

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

Mathematics
Step-by-step answer
P Answered by PhD

The answer is in the image 

The answer is in the image 
Mathematics
Step-by-step answer
P Answered by PhD

The solution is given in the image below

The solution is given in the image below
Mathematics
Step-by-step answer
P Answered by PhD

Here,

tip=18%of $32

tip=(18/100)*32

=0.18*32

=$5.76

Total payment=32+5.76=$37.76

Mathematics
Step-by-step answer
P Answered by PhD

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

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