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Rus_ich [418]
3 years ago
8

What is AC? Giving brainliest

Mathematics
1 answer:
vodka [1.7K]3 years ago
5 0
4/AC = AC/9
AC ^2 = 36
AC = 6
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The circumference of a sphere was measured to be 90 cm with a possible error of 0.5 cm.
Akimi4 [234]

Answer:

Error in the sphere's surface: 29 cm^2  and relative error in surface measure: 0.011

Error in the sphere's volume: 205 cm^3 and relative error in the volume measure: 0.017

Step-by-step explanation:

(a)

The measured length (l) of the circumference is 90 cm with an error of 0.5 cm, that is:

l=2\,\pi\,R=90\,cm\\R=\frac{90}{2\,\pi} \,cm=\frac{45}{\pi} \,cm=14.3239\,\,cm

and with regards to the error:

dl=0.5 \, cm\\dl=2\,\pi\,dR\\dR=\frac{dl}{2\,\pi} =\frac{1}{4\,\pi} cm = 0.0796\,cm

then when we use the formula for the sphere's surface, we get:

S=4\,\pi\,R^2\\dS=4\,\pi\,2\,R\,(dR)\\dS=8\,\,\pi\.(\frac{45}{\pi} \,\,cm)\,(\frac{1}{4\pi}\,cm) =\frac{90}{\pi} \,\,cm^2\approx \,29\,cm^2

Then the relative error in the surface is:

\frac{dS}{S} =\frac{90/\pi}{4\,\pi\,R^2} =\frac{1}{90} =0.011

(b)

Use the formula for the volume of the sphere:

V=\frac{4\,\pi}{3} R^3\\dV=\frac{4\,\pi}{3}\,3\,R^2\,(dR)=4\,\pi\,R^2\,(\frac{1}{4\pi}) \,cm=(\frac{45}{\pi})^2 \,\,cm^3\approx 205\,\,cm^3

Then the relative error in the volume is:

\frac{dV}{V} =\frac{205}{12310.5} \approx 0.017

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Step-by-step explanation:

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