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3 years ago

Find the area of a sector with a central angle of 170° and a diameter of 9.1 cm. Round to the nearest tenth.

2 answers:

6 0

A central angle:
α = 170°
d = 9.1 cm
r = 9.1 : 2 = 4.55 cm
Area of a sector:
A = r² π α / 360°
A = ( 4.55 )² · 3.14 · 170° / 360°
A = 30.7 cm²

ehidna [41]3 years ago

3 0

Answer:

The area of sector is 30.7 cm².

Step-by-step explanation:

The diameter of a circle is 9.1 cm, so the radius of the circle is

$r=\frac{d}{2}=\frac{9.1}{2}=4.55$

The central angle of a sector is 170°.

The area of a sector is

$A=\pi r^2\times (\frac{\theta}{360})$

Where, r is radius and θ is central angle.

$A=\pi (4.55)^2\times (\frac{170}{360})$

$A=30.712777$

$A\approx 30.7$

Therefore the area of sector is 30.7 cm².

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What term is 1/1024 in the geometric sequence,-1,1/4,-1/6..?

Trava [24]

Answer:

$\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}$

Step-by-step explanation:

The explicit formula for a geometric sequence:

$a_n=a_1r^{n-1}$

$a_n$ - n-th term

$a_1$ - first term

$r$ - common ratio

$r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}$

We have

$a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...$

The common ratio:

$r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}$

<h2>It's not a geometric sequence.</h2>

If $a_3=-\dfrac{1}{16}$ then the common ratio is $r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}$

Put to the explicit formula:

$a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}$

Put $a_n=\dfrac{1}{1024}$ and solve for <em>n </em>:

$-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1$

$\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6$

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4 years ago

What is 25/99 simplified

astra-53 [7]

Answer:

i dont think you can simplify it any more

Step-by-step explanation:

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3 years ago

Read 2 more answers

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sdas [7]

Answer:

Option B is correct.

Step-by-step explanation:

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3 years ago

You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distrib

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Answer:

Step-by-step explanation:

Given that that (X) the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds.

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