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2 years ago

Circle O has a circumference of approximately 28.3 cm.

Mathematics

2 answers:

statuscvo [17]2 years ago

3 0

Answer:

A) 4.5 cm

Step-by-step explanation:

Given: Circumference of the circle = 28.3 cm

Here we are asked to find the radius "r".

2.π.r = 28.3

The value of π = 3.14

2*3.14.r = 28.3

6.28r = 28.3

Dividing both sides by 6.28, we get

r = 28.3/6.28

r = 4.5 cm.

The radius of the circle r = 4.5 cm

Answer: A) 4.5 cm

Thank you.

Elza [17]2 years ago

3 0

Circle O has a circumference of approximately 28.3 cm.

What is the approximate length of the radius, r?

4.5 cm

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$\left[0,\dfrac\pi8\right],\left[\dfrac\pi8,\dfrac\pi4\right],\left[\dfrac\pi4,\dfrac{3\pi}8\right],\left[\dfrac{3\pi}8,\dfrac\pi2\right]$

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Midpoint rule

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We first interpolate the integrand over each subinterval by a quadratic polynomial $p_i(x)$ , where

$p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}$

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$\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx$

It so happens that the integral of $p_i(x)$ reduces nicely to the form you're probably more familiar with,

$S_i=\displaystyle\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx=\frac{r_i-\ell_i}6(f(\ell_i)+4f(m_i)+f(r_i))$

Then the integral is approximately

$\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4S_i\approx\boxed{3.000117}$

Compare these to the actual value of the integral, 3. I've included plots of the approximations below.

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