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shepuryov [24]
3 years ago
8

Prove that the two circles shown below are similar. ​

Mathematics
1 answer:
Setler [38]3 years ago
8 0

Answer:

The scale factor is \frac{R_{A}}{R_{C}}=\frac{5}{2}

<u>We can say that both circles are similar.</u>

Step-by-step explanation:

If we move the little circle to the center of the bigger circle, so the <u>translate vector will be (3,5).</u>

Now we realize that the bigger circle is just a dilation of the smaller circle, the<u> scale factor is:</u>

R_{A}=5

R_{C}=2

\frac{R_{A}}{R_{C}}=\frac{5}{2}

Therefore, <u>we can say that both circles are similiar.</u>

<u />

I hope it helps you!

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konstantin123 [22]
Hello! I can help you with this!

a. The function that would best represent Samantha's account is f(5) = 500(1 + 0.04)^5. This is because $500 is the principal, the interest rate is 4%, and we're looking for the amount in the savings account 5 years later.

b. Okay. 1 = 0.04 is 1.04. 1.04^5 is 1.216652902. It's a long decimal, but don't delete it. Multiply that decimal by 500 and you get 608.32645 and other numbers behind it or 608 when rounded to the nearest dollar. Samantha will have about $608 in her savings account in 5 years.

Note: The formula goes like this: f(x) = P(1 + r)^x. This means, you add 1 and the simple interest rate in decimal form together and raise that up by the exponent. There is no shortcuts for this, so you'll have to use the calculator. There will be a very long decimal, but don't clear it. Instead, multiply it by the principal to get the answer. It seems very complicating, but if you do this right, it gets easier overtime and you'll make less errors. There are more complex problems out there, so this formula is very important, but it was kept simple for this question.
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