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2 years ago

A circle has a circumference of 18 cm. What is the length of an arc that has a measure of 160°?

Mathematics

1 answer:

Kay [80]2 years ago

5 0

Answer:

$8\:\mathrm{cm}$

Step-by-step explanation:

By definition, the length arc is a portion of a circle's circumference. The exact amount is directly proportional to the measure of the arc. Therefore, the formula for the length of an arc with measure (in degrees) $\theta$ is $2\pi r\cdot \frac{\theta}{360}$ , where $2\pi r$ is the circumference of the circle.

Substituting $2\pi r=18$ and $\theta=160^{\circ}$ :

$L_{arc}=18\cdot \frac{160}{360}=\boxed{8\:\mathrm{cm}}$

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Step-by-step explanation:

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2 years ago

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boyakko [2]

Answer:

$(x,y) =(-4,-3)$ --- Vertex

$x = -4$ --- Axis of symmetry

Step-by-step explanation:

Given

$y = -6(x + 4)^2 - 3$

Solving (a): The vertex

For an equation written in

$y = a(x - h)^2 + k$

The vertex is:

$(x,y) = (h,k)$

By comparison:

$y = a(x - h)^2 + k$ and $y = -6(x + 4)^2 - 3$

$-h =4$ $k = -3$

$h =-4$ $k = -3$

So, the vertex is:

$(x,y) =(-4,-3)$

Solving (b): The axis of symmetry

For an equation written in

$y = a(x - h)^2 + k$

The axis of symmetry is:

x = h

In (a):

$h =-4$

So:

$x = -4$

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2 years ago

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3 years ago

Read 2 more answers

Solve 3x² + 4x = 2. (2 points)

uysha [10]

Answer:

Step-by-step explanation:

As it is a second order equation, it means that it has two possible answers and they are $x_1$ and $x_2$ .

The famous quadratic formula for solving any second order equation is the following:

$x_{1} = \frac{-b + \sqrt{b^2 - 4 ac}}{2a}\\x_{2}=\frac{-b - \sqrt{b^2 - 4 ac}}{2a}$

Where a is the coefficient of $x^2$ , b is the coefficient of x, and c is the free term. In other words,

$a = 3\\b=4\\c=-2$

as the equation should be in the following form:

$a x^2 + bx+c = 0$

Therefore the possible answer should be the following,

$\frac{-4 + \sqrt{4^2 - 4*3*(-2)}}{2*3}=\frac{-4 +\sqrt{16 + 24}}{6} =\frac{-4 + \sqrt{40}}{6}=\\ \frac{-4 + \sqrt{4*10}}{6} = \frac{-4 + 2\sqrt{10}}{6}$ $\frac{2*(-2 + \sqrt{10})}{2*3} = \frac{-2 + \sqrt{10}}{3}$