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2 years ago

Given: Circle X with a Radius r and circle Y with radius s Prove: Circle x is similar to circle y

Mathematics

2 answers:

lana [24]2 years ago

8 0

Two figures are similar if one is the scaled version of the other.

This is always the case for circles, because their geometry is fixed, and you can't modify it in anyway, otherwise it wouldn't be a circle anymore.

To be more precise, you only need two steps to prove that every two circles are similar:

Translate one of the two circles so that they have the same center
Scale the inner circle (for example) unit it has the same radius of the outer one. You can obviously shrink the outer one as well

Now the two circles have the same center and the same radius, and thus they are the same. We just proved that any two circles can be reduced to be the same circle using only translations and scaling, which generate similar shapes.

Recapping, we have:

Start with circle X and radius r
Translate it so that it has the same center as circle Y. This new circle, say X', is similar to the first one, because you only translated it.
Scale the radius of circle X' until it becomes $s$ . This new circle, say X'', is similar to X' because you only scaled it

So, we passed from X to X' to X'', and they are all similar to each other, and in the end we have X''=Y, which ends the proof.

stealth61 [152]2 years ago

5 0

Answer:

Step-by-step explanation:

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David drove a distance of 187km, correct to 3 significant figures. He used 28 litres of petrol, correct to 2 significant figures

mote1985 [20]

David drove a distance (d) of 187km, to 3 significant figures. He used 28 litres of petrol (p), to 2 significant figures.
The petrol consumption (c) in km per litre is given by the formula: c= d/p
By considering bounds, work out the value of c, to a suitable degree of accuracy. You must show your working and give a reason for your answer. I'm not totally comfortable with sig figs, but I believe that the answer can only be expressed as accurately as least number of sig figs of any data used in the computations.....thus ....the answer should be rounded to 2 sig figs

So

187 / 28 = 6.67 ⇒ 6.7 km / L [rounded to 2 sig figs ].

8 0

2 years ago

Read 2 more answers

Vugar has a maximum of 30 batteries for toys. Each toy helicopter uses the same number of batteries, and each toy car uses the s

Leno4ka [110]

Answer: 3H+4C<_ 30

The coefficients of the variables H and C represent the number of batteries each toy helicopter and each toy car uses.

Step-by-step explanation:

Each toy helicopter uses 3 batteries, and each toy car uses 4 batteries.

Now let's check whether Vugar has enough batteries for 5 toy helicopters and 4 toy cars. To do this, we substitute H=5 and C= 4 in the given inequality:

Does Vugar have enough batteries to play with 5 toy helicopters and 4 toy cars?

No, because if you plug in the value for H and C:

3H + 4C<_ 30

3(5) + 4(4) <_30

15 + 16 <_ 30

31 <_ 30; false

Since the inequality is false, Vugar does not have enough batteries to play with 555 toy helicopters and 444 toy cars.

Each toy helicopter uses 333 batteries, and each toy car uses 444 batteries.

No, Vugar does not have enough batteries to play with 555 toy helicopters and 444 toy cars.

6 0

2 years ago

Read 2 more answers

A circular city plaza is surrounded by a row of bricks. The area of the plaza is 1,520 square meters. How long is the row of bri

Korolek [52]

Answer:

138 meters

Step-by-step explanation:

step 1

Find the radius of the circular city plaza

The area is equal to

$A=\pi r^{2}$

we have

$A=1,520\ m^2$

$\pi =3.14$

substitute

$1,520=(3.14)r^{2}$

solve for r

$r^2=1,520/3.14\\r=22\ m$

step 2

we know that

To find out how long is the row of bricks, determine the circumference of the circular city plaza

The circumference is equal to

$C=2\pi r$

we have

$r=22\ m$

$\pi =3.14$

substitute

$C=2(3.14)(22)=138\ m$

8 0

2 years ago

The area of a plot of land is 2496 square meters. A small part of the land is fenced. The ratio of the area of the plot of land

AfilCa [17]

My late response (haha): First, you would write a proportion.

Step 1: 2496 over 48 = x over 31
(x represents the area of the land that is not fenced).

Step 2: Cross multiply
2496 times 31 and x times 48

Step 3: Calculate
77376 = 48x

Step 4: Divide both sides by 48
77376/48 = 1612
48x/48 = x

Step 5: Write it as a sentence
The area of the land that is not fenced is 1612 squared meters.

Hope that helped! Good luck! :]

4 0

2 years ago

Horatio is solving the equation Negative three-fourths + two-fifths x = StartFraction 7 Over 20 EndFraction x minus one-half. Wh

nata0808 [166]

Answer:

x = 5

Step-by-step explanation:

Step 1: Write equation

-3/4 + 2/5x = 7/20x - 1/2

Step 2: Subtract 7/20x on both sides

-3/4 + 1/20x = -1/2

Step 3: Add 3/4 to both sides

1/20x = 1/4

Step 4: Divide 1/20 on both sides

x = 5

6 0

2 years ago