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2 years ago

A circle with circumference 18 had an arc with 120 central angle. what is the length of the arc

Mathematics

2 answers:

lawyer [7]2 years ago

5 0

Answer:

A circle with circumference 18 had an arc with 120 central angle.

=> Radius of that circle: R = 18/(2 x pi) = 2.86

=> Length of that arc: L = R x 120 x pi/180 = 2.86 x (2/3) x pi = 5.99

Hope this helps!

labwork [276]2 years ago

4 0

Answer:

Step-by-step explanation:

Angle: arc length

360 : 18

120 : X

X/120 = 18/360

X = 120 × 18/360

X = 6

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Write the equation in standard form. Identity the center and radius. x² + y2 + 8x-4y-7=0

lorasvet [3.4K]

Answer:

equation;

$(x + 4) {}^{2} + (y - 2) {}^{2} = 27$

Center (-4,2)

Radius is

$3 \sqrt{3}$

Step-by-step explanation:

Since the x^2 and y^2 have the same coeffiecent this will be a circle in a form of

$(x - h) {}^{2} + (y - k) {}^{2} = {r}^{2}$

Where (h,k) is center

r is the radius

So first we group like Terms together

${x}^{2} + 8x + {y}^{2} - 4y - 7 = 0$

Add 7 to both sides

${x}^{2} + 8x + {y}^{2} - 4y = 7$

$( {x}^{2} + 8x) +( {y}^{2} - 4y) = 7$

Since the orginal form of the equation of the circle has a perfect square we need to complete the square for each problem

$(\frac{8}{2} ) {}^{2} = 16$

and

$( - \frac{4}{2} ) {}^{2} = 4$

so we have

${x}^{2} + 8x + 16 + {y}^{2} - 4y + 4y = 7 + 16 + 4$

${x}^{2} + 8x + 16 + {y}^{2} - 4y + 4y = 27$

$(x + 4) {}^{2} + (y - 2) {}^{2} = 27$

To find our center, h is -4 and k is 2

so the center is (-4,2)

The radius is

$\sqrt{27} = 3 \sqrt{3}$

So the radius is 3 times sqr root of 3.

8 0

2 years ago

Use the net as an aid to compute the surface area (rounded to the nearest integer) of the triangular pyramid with an equilateral

aleksandrvk [35]

Answer:

Correct answer is $C)\ 254\ m^{2}$

Step-by-step explanation:

As per the given diagram, we know the following details:

Height of the triangular pyramid is 14m.

Side of base = 10m

Height of Triangular base = 8.7m

Formula for surface area of triangular pyramid:

$\text{Area = Area of Triangular base + 3 }\times\text{Area of side triangle}$

(Triangular base is shown in the dotted lines in the question figure.

The other 3 triangles are the side triangles.)

We know that,

$\text{Area of a triangle = }\dfrac{1}{2} \times \text{Base} \times \text{Height}$

$\Rightarrow \text{Required Surface Area = } \dfrac{1}{2} \times 8.7 \times 10 + 3 \times \dfrac{1}{2} \times 14 \times 10\\\Rightarrow \dfrac{1}{2}\times (87 + 3 \times 140)\\\Rightarrow \dfrac{1}{2}\times (87 + 420)\\\Rightarrow \dfrac{1}{2} \times 507\\$\approx$ 254 m^{2}$

Hence correct answer is $C)\ 254\ m^{2}$ .

3 0

2 years ago

Solve for x triangles

wel

Answer:

115

Step-by-step explanation:

180-50=130

130/2=65

180-65=115

4 0

2 years ago

1.73639 rounded to the nearest thousanth

Maurinko [17]

^ is in the thousadths place so look for the number before it, which is 3. 3 is less than 5 so 6 stays as is so it becomes 1.736

8 0

3 years ago

Sarah is collecting recyclables for a science project. on the first day she collects 35 recyclable objects. on the second day sh

Svet_ta [14]

The scneario here expressed is an aritmetic sequence because it can be explained like this:

a1=35
an=an−1+17

So all the variables can fit in and will be better explained than a geometric sequence in which you need a common ratio and that is not needed in this case

4 0

2 years ago

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