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2 years ago

The circumference of a circle is about 50 centimeters (cm). Which is closest to the length of its radius? You may use 3.14 for

Mathematics

1 answer:

Romashka-Z-Leto [24]2 years ago

5 0

Answer:

8 cm

Step-by-step explanation:

The formula of circumference is c= πd------(1)

where C = circumference, π = 3.14 and d = diameter

as we know that diameter is equal to d= 2r

put the diameter formula in eq(1)

we get c= π2r-------(2)

from eq (2) separate r means radius

hence, r= c/(π2)------(3)

put the values in eq(3)

and radius is equal to 8 cm.

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3 years ago

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2 years ago

How are exponents and radicals used to present roots of real numbers

MissTica

Answer:

$\sqrt[n]{a} =a^{\frac{1}{n}}$

Explanation:

Roots of real numbers can be represented by radicals or by exponents.

First, I present some examples to show how exponents and radicals are related, and then generalize.

$\sqrt{4}=4^{(\frac{1}{2})}=(2^2)^\frac{1}{2}=(2)^{\frac{2}{2}}=2^1=2\\\\\\\sqrt{25}=(25)^{\frac{1}{2}}=(5^2)^{\frac{1}{2}}=(5)^{\frac{2}{2}}=5^1=5$

$\sqrt[3]{8}=(8)^{\frac{1}{3}}=(2^3)^{\frac{1}{3}}=(2)^{\frac{3}{3}}=2^1=2$

When you write 5² = 25, then 5 is the square root of 25.

And in general, if n is a positive integer and $a^n=x$ , then $a$ is the nth root of x.

Also, if n even (and positive) and $a$ is positive, then $a^{\frac{1}{n}}$ is the positive nth root of $a$

Thus,

$\sqrt[n]{a} =a^{\frac{1}{n}}$

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3 years ago