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4 years ago

5. If the area of the circle is 81π units?, what is the circumference of the circle?

Mathematics

1 answer:

olga_2 [115]4 years ago

5 0

Answer:

The circumference of the circle is 18π.

Step-by-step explanation:

First you have to acknowledge the equation on how to find the area of a circle. Which is A = πr².

Next you put 81π = πr².

Then you divide π from 81 to the other side and that should eliminate π from both sides.

Now you are left with 81 = r². Which if you square 81, it would become ±9. It would most likely be a positive 9.

So now you just add 9+9 to get the diameter because to get the circumference you need to know the equation to get it, which is diameter x π.

The full answer could be 18π or the simplified version which is estimated to the nearest hundredth which is 56.55.

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Proof that : <img src="https://tex.z-dn.net/?f=%20%7Bsin%7D%5E%7B2%7D%20%5Ctheta%20%2B%20%20%7Bcos%7D%5E%7B2%7D%20%5C%3A%5Cth

Arisa [49]

Answer:

Solution given:

Right angled triangle ABC is drawn where <C= $\theta$

we know that

$\displaystyle Sin\theta=\frac{opposite}{hypotenuse} =\frac{AB}{AC}$

$\displaystyle Cos\theta=\frac{adjacent}{hypotenuse}=\frac{BC}{AC}$

Now

left hand side

$\displaystyle {sin}^{2} \theta + {cos}^{2} \:\theta$

Substituting value

$(\frac{AB}{AC})²+(\frac{BC}{AC})²$

distributing power

$\frac{AB²}{AC²}+\frac{BC²}{AC²}$

Taking L.C.M

$\displaystyle \frac{AB²+BC²}{AC²}$ ....[I]

In ∆ABC By using Pythagoras law we get

$\boxed{\green{\bold{Opposite²+adjacent²=hypotenuse²}}}$

AB²+BC²=AC²

Substituting value of AB²+BC² in equation [I]

we get

$\displaystyle \frac{AC²}{AC²}$

Right hand side

<h3>proved</h3>

8 0

3 years ago

Read 2 more answers

Given the expression: 3x10 − 48x2

BartSMP [9]

Factorization involves representing an expression with smaller terms.

When the greatest common factor is factored out, the equivalent expression is: $3x^2(x^8 - 16)$ .
The complete factored expression is: $3x^2(x^4 - 4)(x^4 + 4)$

The expression is given as:

$3x^{10} -48x^2$

The GCF of $3x^{10}$ and $48x^2$ is $3x^2$ .

So, we have:

$3x^{10} -48x^2 = 3x^2 \times x^8 - 3x^2 \times 16$

Factor out $3x^2$

$3x^{10} -48x^2 = 3x^2(x^8 - 16)$

To factorize the expression completely, we express $x^8$ and $16$ as squares.

So, we have:

$3x^{10} -48x^2 = 3x^2((x^4)^2 - 4^2)$

Apply difference of two squares

$3x^{10} -48x^2 = 3x^2(x^4 - 4)(x^4 + 4)$

So, the complete factor of $3x^{10} -48x^2$ is $3x^2(x^4 - 4)(x^4 + 4)$

Read more about factorization at:

brainly.com/question/19386208

3 0

2 years ago

Find the x and y intercepts 8x-4y= -16

scZoUnD [109]

$8x-4y=-16\\\\x-intercept\ for\ y=0:\\\\8x-4(0)=-16\\\\8x-0=-16\\\\8x=-16\qquad\text{divide both sides by 8}\\\\\boxed{x=-2\to(-2,\ 0)}\\\\y-intercept\ for\ x=0:\\\\8(0)-4y=-16\\\\0-4y=-16\\\\-4y=-16\qquad\text{divide both sides by (-4)}\\\\\boxed{y=4\to(0,\ 4)}$

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3 years ago

What is the slope of the line segment?A graph is shown. The values on the x axis are 0, 1, 2, 3, 4, and 5. The values on the y a

victus00 [196]

The slope = y value / corresponding x value

use the point (3,15)

slope = 15 / 3 = 5

6 0

4 years ago

Read 2 more answers

Which statement describes the behavior of the function f (x) = StartFraction 2 x Over 1 minus x squared EndFraction?

Daniel [21]

Answer:

Second option: the graph approaches 0 as x approaches infinity.

Explanation:

The function f(x) is:

$f(x)=\frac{2x}{1-x^2}$

When x approach infinity the term x² grows rapidly (more rapid than x), thus 1 - x², which is in the denominator will decrease, become a large negative more rapid than the x in the numerator. Thus you can expect that the function approaches zero.

To prove that in a more analytical way, divide both numerator and denominator by x and simplifiy:

$\lim_{x \to \infty} \frac{2x}{1-x^2}\\\\ \lim_{x \to \infty} \frac{2x/x}{(1-x^2)/x}\\\\ \lim_{x \to \infty} \frac{2}{1/x-x}\\\\\lim_{x \to \infty} \frac{2}{0-x}\\ \\ \lim_{x \to \infty} \frac{2}{-x}\\ \\ \lim_{x \to \infty} -\frac{2}{x}=0$

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3 years ago

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5. If the area of the circle is 81π units?, what is the circumference of the circle?​

5. If the area of the circle is 81π units?, what is the circumference of the circle?