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4 years ago

A circle with circumference 6 has an arc of 60 degrees central angle. What is the length of the arc

Mathematics

1 answer:

nata0808 [166]4 years ago

7 0

The length of the arc is 1.06m. hope that helps!

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Please help radical expression dividing

77julia77 [94]

$\bf \cfrac{\sqrt[4]{63}}{4\sqrt[4]{6}}\qquad 
\begin{cases}
63=3\cdot 3\cdot 7\\
6=2\cdot 3
\end{cases}\implies \cfrac{\sqrt[4]{3\cdot 3\cdot 7}}{4\sqrt[4]{2\cdot 3}}\implies \cfrac{\underline{\sqrt[4]{3}}\cdot \sqrt[4]{3}\cdot \sqrt[4]{7}}{4\sqrt[4]{2}\cdot \underline{\sqrt[4]{3}}}
\\\\\\
\cfrac{\sqrt[4]{3}\cdot \sqrt[4]{7}}{4\sqrt[4]{2}}\implies \cfrac{\sqrt[4]{3\cdot 7}}{4\sqrt[4]{2}}\implies \cfrac{\sqrt[4]{21}}{4\sqrt[4]{2}}$

$\bf \textit{now, rationalizing the denominator}\\\\
\cfrac{\sqrt[4]{21}}{4\sqrt[4]{2}}\cdot \cfrac{\sqrt[4]{2^3}}{\sqrt[4]{2^3}}\implies \cfrac{\sqrt[4]{21}\cdot \sqrt[4]{8}}{4\sqrt[4]{2}\cdot \sqrt[4]{2^3}}\implies \cfrac{\sqrt[4]{21\cdot 8}}{4\sqrt[4]{2\cdot 2^3}}\implies \cfrac{\sqrt[4]{168}}{4\sqrt[4]{2^4}}
\\\\\\
\cfrac{\sqrt[4]{168}}{4\cdot 2}\implies \cfrac{\sqrt[4]{168}}{8}$

and is all you can simplify from it.

so... all we did, was rationaliize it, namely, "getting rid of the pesky radical at the bottom", we do so by simply multiplying it by something that will raise the radicand, to the same degree as the root, thus the radicand comes out.

6 0

3 years ago

Y = 3 sin2x, y = 0, 0 ≤ x ≤ π; about the x−axis

Dominik [7]

I assume you're revolving the region with those bounds about the x-axis, and supposed to find the volume.

Via the disk method,

$\displaystyle\pi\int_0^\pi(3\sin2x)^2\,\mathrm dx=9\pi\int_0^\pi\sin^22x\,\mathrm dx$

Recall the half-angle identity for sine:

$\sin^2t=\dfrac{1-\cos2t}2$
$\implies\displaystyle\frac{9\pi}2\int_0^\pi(1-\cos4x)\,\mathrm dx$
$=\displaystyle\frac{9\pi}2\left(x-\frac14\sin4x\right)\bigg|_{x=0}^{x=\pi}$
$=\dfrac{9\pi^2}2$

8 0

3 years ago

A carpet in Frank's house has a length of 2 1/4 meters and a width of 1 1/5 meters. What is the perimeter of the carpet?

stich3 [128]

Answer:

4.5+2.4=6.9

Step-by-step explanation:

Fraction form: 69/10

6 0

3 years ago

Read 2 more answers

17. What is the area of the figure below?

Sidana [21]

If length of rectangle is 8 cm, breadth is 4 cm, side of square is 3 cm, base of triangle is 3 cm, then the area of figure will be 48.5 $cm^{2}$ .

Given that length of rectangle is 8 cm, Breadth of rectangle is 4 cm,side of square is 3 cm,base of right angled triangle is 3 cm,height of triangle is 5 cm.

Area of figure=Area of rectangle+Area of square+Area of triangle

Area of rectangle=length*breadth

Area of square=Side*Side

Area of triangle=1/2 *Base*Height

Area of figure=8*4+3*3+1/2 *3*5

=32+9+1/2 *15

=41+15/2

=(82+15)/2

=97/2

=48.5 $cm^{2}$

Hence if length of rectangle is 8 cm, breadth is 4 cm, side of square is 3 cm, base of triangle is 3 cm, then the area of figure will be 48.5 $cm^{2}$ .

Learn more about area at brainly.com/question/25292087

#SPJ9

7 0

2 years ago

8 + (-3) integers topic

dalvyx [7]

If you’re asking for the answer, it’s 5

3 0

3 years ago