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Maksim231197 [3]
3 years ago
9

The radius of a circle is 3 miles. What is the length of a 90° arc?

Mathematics
1 answer:
stealth61 [152]3 years ago
3 0

Answer:

The length of the arc is 4.6375 miles

Step-by-step explanation:

Firstly, find the perimeter of the circle by doing 2*pi*r, you'll get about 18.55 miles.

2*pi*r ---> 2*pi*3 ---> 6*pi ---> ≈ 18.55 miles

Next, plug in x/360, where 360 is the total arc of a circle, and x is the arc you need.

x/360 ---> 90/360 ---> = 0.25

Lastly multiply the two numbers.

18.55 * 0.25 ---> 4.6375 miles is your answer.

<em>(you may need to round your answer if needed)</em>

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5 x 3²⁴  bacteria will there be after one day.

What is exponents?

Exponentiation could be a calculation, written as bⁿ, involving 2 numbers, the bottom b and also the exponent or power n, and pronounced as "b to the n".

Consider what is actually happening in the question.

You begin with 5 bacteria, and after 1 hour it has tripled so you now have

5x 3=15.

Next hour, it triples again so you now have 5 x 3 x 3=45

You can see the pattern shows that the number of bacteria is multiplying every hour by a factor of 3. An exponent denotes how many times we are multiplying a number by itself, for example: 3⁴  means we are multiplying the number 3 a total of 4 times (3 x 3 x 3 x 3).

Therefore the question is requiring us to triple the number of bacteria every hour for 24 hours, which means we are multiplying by 3 a total of 24 times. This gives us:

n x 324 where n is the number of bacteria you begin with.

Since you begin with 1 bacteria, the solution is 5 x 3²⁴.

Hence 5 x 3²⁴  bacteria will there be after one day.

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