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Julli [10]
2 years ago
13

There is a constant ratio between corresponding sides of similar figures. Since circles don't have sides, what ratio(s) could yo

u use to prove that all circles are similar?
Mathematics
2 answers:
inessss [21]2 years ago
7 0
A circle's size and shape is fully defined by its radius. Given two circles with radii r and r', the diameters are d=2r and d'=2r' and they are in the ratio 

<span>d'/d = (2r')/(2r) = r'/r. </span>

<span>The diameter ratio is the same as the radius ratio. Similarly, the circumferences c=πd and c' = πd' are in the ratio </span>

<span>c'/c = (πd')/(πd) = d'/d = r'/r </span>

<span>The circumference ratio is the same as the diameter ratio and the radius ratio. All of the key linear dimensions are in the same proportion. </span>

<span>You might point out that the same thing happens with a square, where the size and shape are also completely determined by a single measurement, the length s of a side, with the diagonal and perimeter (corresponding to diameter and circumference) being d = √2 s and p = 4s. </span>

<span>Maybe you can lead at least some of the students to generalize to other regular polygons. Some of them (like the equilateral triangle and regular hexagon) can be demonstrated like the square and circle above with formulas from geometry. The general case needs trig ratios to state the formulas relating side length to the radius and apothem of the polygon.</span>
hodyreva [135]2 years ago
5 0

Answer:

The ratio of circumference to diameter in all circles is a constant value, pi. Also, the ratio of the diameters and the ratio of the circumferences of any two circles reduces to the ratio of their radii.

Step-by-step explanation:

just answered question, answer above is what it said to be a possible answer

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Jug A has 0.1 litres more than jug B. Jug C has 200 millilitres less than jug B. Jug D has ¼ of the amount that is in jug A. The
Gnesinka [82]

Answer:

A = 0.8 litres

B = 0.7 litres

C = 0.5 litres

D = 0.2 litres

Step-by-step explanation

Here's what we know:

1. Jug A = B + .1 litres

2. Jug C = B - 200 (or 0.2 litres)

3. Jug D = .25 x A

4. Jug A + Jug B = 1.5 litres

In problem 1, we learned that Jug A has .1 litres more than Jug B and in problem 4, the two of them added together are 1.5 litres. To solve this we can combine the problems.  

B + .1 litres + B = 1.5 litres

2B + .1 = 1.5

Subtract .01 from each side and you have 2B = 1.4

Divide each side by 2 and you have B = 0.7 litres

Plug this info into problem 1 and you can solve for A. (0.7 + 0.1 = 0.8)

Plug this info into problem 2 and you can solve for C. (0.7 - 0.2 = 0.5)

Since you have A, you can use that info to solve problem 3 (0.25 x 0.8 = 0.2)

8 0
2 years ago
What is the solution to the equation below?
MakcuM [25]

Answer:

X=4

Step-by-step explanation:

The solution is in the file

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2 years ago
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6 1/4 :) Is this correct?

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The height of Mountain P is 1,086 feet.The height of Mountain Q is 4 times the height of Mountain P.The area model shown below r
earnstyle [38]

Answer:

A=4000, B=80, C=24

Step-by-step explanation:

You forgot to put the correct area model, I attached it to the answer.

We have the fact that Mountain Q is 4 times the height of Mountain P. That's the "4" we have in the left side of our model. It's like having a multiplication table, next to the "4" we have "A" and upper this we have "1000", the only thing we have to do is multiplify 4*1000=4000. The next letter we have is B and below it we have "320", we divided it by 4, 320/4=80. The last letter we have is C, and is below a "6", we only have to multiplify it by 4, 6*4=24.

At the end we only sum our

  • A + 320 + c = 4344 (4 times the height of Mountain P).
  • 1000 + B + 6 = 1086(the height of the Mountain P).

8 0
2 years ago
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