Find the arc length of the partial circle.

Mathematics

1 answer:

Serga [27]3 years ago

5 0

Known :

r = 5 cm

θ = 360° - 90° = 270°

Asked :

Arc length of the partial circle = ...?

Answer :

Arc length

$= \frac{θ}{360} \times 2\pi r \\ = \frac{270}{360} \times 2 \times 3.14 \times 5 \\ = \frac{3}{4} \times 31.4 \\ = \frac{3}{4} \times \frac{314}{10} \\ = \frac{942}{40} \\ = 23.55 \: cm$

So, the arc length of the partial circle is 23,55 cm

Hope it helps and is useful :)

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3 years ago

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GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola: $y=3x^2-4$

Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

(where (h, k) is the vertex and $a$ is some constant)

Substitute point (0, -4) into the equation:

$\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}$

Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$