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3 years ago

I NEED HELP ASAP!!!!

Mathematics

1 answer:

GuDViN [60]3 years ago

7 0

Answer:

the first one

Step-by-step explanation:

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The measurenicnt of the circumference of a circle is found to be 56 centimeters. The possible error in measuring the circumferen

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Answer:

(a) Approximate the percent error in computing the area of the circle: 4.5%

(b) Estimate the maximum allowable percent error in measuring the circumference if the error in computing the area cannot exceed 3%: 0.6 cm

Step-by-step explanation:

(a)

First we need to calculate the radius from the circumference:

$c=2\pi r\\r=\frac{c}{2\pi } \\c=8.9 cm$

I leave only one decimal as we need to keep significative figures

Now we proceed to calculate the error for the radius:

$\Delta r=\frac{dt}{dc} \Delta c\\\\\frac{dt}{dc} = \frac{1}{2 \pi } \\\\\Delta r=\frac{1}{2 \pi } (1.2)\\\\\Delta r= 0.2 cm$

$r = 8.9 \pm 0.2 cm$

Again only one decimal because the significative figures

Now that we have the radius, we can calculate the area and the error:

$A=\pi r^{2}\\A=249 cm^{2}$

Then we calculate the error:

$\Delta A= (\frac{dA}{dr} ) \Delta r\\\\\Delta A= 2\pi r \Delta r\\\\\Delta A= 11.2 cm^{2}$

$A=249 \pm 11.2 cm^{2}$

Now we proceed to calculate the percent error:

$\%e =\frac{\Delta A}{A} *100\\\\\%e =\frac{11.2}{249} *100\\\\\%e =4.5\%$

(b)

With the previous values and equations, now we set our error in 3%, so we just go back changing the values:

$\%e =\frac{\Delta A}{A} *100\\\\3\%=\frac{\Delta A}{249} *100\\\\\Delta A =7.5 cm^{2}$

Now we calculate the error for the radius:

$\Delta r= \frac{\Delta A}{2 \pi r}\\\\\Delta r= \frac{7.5}{2 \pi 8.9}\\\\\Delta r= 0.1 cm$

Now we proceed with the error for the circumference:

$\Delta c= \frac{\Delta r}{\frac{1}{2\pi }} = 2\pi \Delta r\\\\\Delta c= 2\pi 0.1\\\\\Delta c= 0.6 cm$

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3 years ago