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1 year ago

PLEASE HELP!

Mathematics

1 answer:

makvit [3.9K]1 year ago

8 0

Answer:

Step-by-step explanation:

diameter = 12 cm

r = 12 ÷ 2 = 6 cm

h = 6 cm

$\sf \boxed{\text{\bf Volume of cone = $\dfrac{1}{3} \pi r^2h$ }}$

$\sf = \dfrac{1}{3}*3.14*6*6*6\\\\ = 226.08 \ cm^3$

To find the surface area, we need to find the slant 'l'

$\sf l = \sqrt{h^2+r^2}\\\\ =\sqrt{6^2+6^2}\\\\ = \sqrt{36+36}\\\\ =\sqrt{72}\\\\= 8.49 \ cm$

$\sf \boxed{\text{\bf Total surface area of cone = $\pi r(r+l)$}}$

= 3.14 * 6 * (6 + 8.49)

= 3.14 * 6 * 14.49

= 273 cm²

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∴ The average rate of f = $\frac{f(2 \pi)-f( \frac{3 \pi}{2} )}{2 \pi - \frac{3 \pi}{2} } = \frac{0-(-2)}{ \frac{\pi}{2} }= \frac{2}{ \frac{\pi}{2} } = \frac{4}{\pi}$

(2) the second function g(x)
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∴ The average rate of g = $\frac{g(2 \pi)-g( \frac{3 \pi}{2} )}{2 
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(3) the third function h(x) = 6 sin x +1
∴ h(3π/2) = 6 sin (3π/2) + 1 = 6 *(-1) + 1 = -5
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∴ The average rate of h = $\frac{f(2 \pi)-f( \frac{3 \pi}{2} )}{2 
\pi - \frac{3 \pi}{2} } = \frac{1-(-5)}{ \frac{\pi}{2} }= \frac{6}{ 
\frac{\pi}{2} } = \frac{12}{\pi}$

By comparing the results, The <span>function which has the greatest rate of change is h(x)
</span>

So, the correct answer is option <span>C) h(x)</span>

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