All categories

3 years ago

If a circle has a diameter of 30 meters, which expression gives its area in

Mathematics

1 answer:

sattari [20]3 years ago

3 0

Answer:

C. 15²π

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Geometry

Diameter: d = 2r
Area of a Circle: A = πr²

Step-by-step explanation:

Step 1: Define

d = 30 m

Step 2: Find Area

Substitute [D]: 30 m = 2r
Isolate r: 15 m = r
Rewrite: r = 15 m
Substitute [AC]: A = π(15 m)²
Rearrange: A = 15²π

You might be interested in

A tire has a radius of 13 inches. Which equation could be used to find the circumference of the tire

pav-90 [236]

Answer:

the tire should be 16 inches in diameter

a way that you can find diameter is if you are given the radius and you just multiply that number by 2 or ADD the same number because usually it is half of the diameter

6 0

2 years ago

The factor tree for 1,764 is shown.

Rashid [163]

Answer:

Step-by-step explanation:

|--------------1764------------|

| |

2 |-------882-----------|

| |

2 |--------441------|

| |

|------9-----| |----49---|

| | | |

3 3 7 7

From the factor tree we see that

$1764 = 2^2 \times 3^3 \times 7^2$

Now we need to find the square root of 1764.

$\sqrt{1764} = \sqrt{2^2 \times 3^2 \times 7^2} = \sqrt{(2 \times 3 \times 7)^2} = \sqrt{(42)^2} = 42$

4 0

3 years ago

Read 2 more answers

A critic randomly selects a movie to review from 3 action movies , 4 comedies , and two dramas . What is the probability that th

seropon [69]

Answer:

4/9

There are a total of 9 movies to choose from. 4 of them are comedy. So the chance you will pick a comedy is 4 out of nine.

7 0

3 years ago

Write a fraction that is less than 1/3 using 1 as a numerator. Then explain why the answer you chose is less than 1/3.

sammy [17]

1/4, because in 1/3, you would only need 3 parts to get one whole, but in 1/4, you would need 4 parts to get a whole.

3 0

3 years ago

I need help with this problem from the calculus portion on my ACT prep guide

LenaWriter [7]

Given a series, the ratio test implies finding the following limit:

$\lim _{n\to\infty}\lvert\frac{a_{n+1}}{a_n}\rvert=r$

If r<1 then the series converges, if r>1 the series diverges and if r=1 the test is inconclusive and we can't assure if the series converges or diverges. So let's see the terms in this limit:

$\begin{gathered} a_n=\frac{2^n}{n5^{n+1}} \\ a_{n+1}=\frac{2^{n+1}}{(n+1)5^{n+2}} \end{gathered}$

Then the limit is:

$\lim _{n\to\infty}\lvert\frac{a_{n+1}}{a_n}\rvert=\lim _{n\to\infty}\lvert\frac{n5^{n+1}}{2^n}\cdot\frac{2^{n+1}}{\mleft(n+1\mright)5^{n+2}}\rvert=\lim _{n\to\infty}\lvert\frac{2^{n+1}}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^{n+1}}{5^{n+2}}\rvert$

We can simplify the expressions inside the absolute value:

$\begin{gathered} \lim _{n\to\infty}\lvert\frac{2^{n+1}}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^{n+1}}{5^{n+2}}\rvert=\lim _{n\to\infty}\lvert\frac{2^n\cdot2}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^n\cdot5}{5^n\cdot5\cdot5}\rvert \\ \lim _{n\to\infty}\lvert\frac{2^n\cdot2}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^n\cdot5}{5^n\cdot5\cdot5}\rvert=\lim _{n\to\infty}\lvert2\cdot\frac{n}{n+1}\cdot\frac{1}{5}\rvert \\ \lim _{n\to\infty}\lvert2\cdot\frac{n}{n+1}\cdot\frac{1}{5}\rvert=\lim _{n\to\infty}\lvert\frac{2}{5}\cdot\frac{n}{n+1}\rvert \end{gathered}$

Since none of the terms inside the absolute value can be negative we can write this with out it:

$\lim _{n\to\infty}\lvert\frac{2}{5}\cdot\frac{n}{n+1}\rvert=\lim _{n\to\infty}\frac{2}{5}\cdot\frac{n}{n+1}$

Now let's re-writte n/(n+1):

$\frac{n}{n+1}=\frac{n}{n\cdot(1+\frac{1}{n})}=\frac{1}{1+\frac{1}{n}}$

Then the limit we have to find is:

$\lim _{n\to\infty}\frac{2}{5}\cdot\frac{n}{n+1}=\lim _{n\to\infty}\frac{2}{5}\cdot\frac{1}{1+\frac{1}{n}}$

Note that the limit of 1/n when n tends to infinite is 0 so we get:

$\lim _{n\to\infty}\frac{2}{5}\cdot\frac{1}{1+\frac{1}{n}}=\frac{2}{5}\cdot\frac{1}{1+0}=\frac{2}{5}=0.4$

So from the test ratio r=0.4 and the series converges. Then the answer is the second option.

8 0

1 year ago