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Annette [7]
3 years ago
9

6. The ratio of the height to the width of a packaging label is 5 to 19. If the height of the label is 2.5

Mathematics
1 answer:
Ahat [919]3 years ago
8 0

Answer:

9.5 inches width

Step-by-step explanation:

solve it using the proportion method

height/ width = 5/19

so let the width be x

so if         height: width:: height: width

                   5   :   19    ::      2.5 :   x

product of extremes = product of means

   5 x  x      =  19 x 2.5

    x=      47.5/5

    x=   9.5 inches (width )

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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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(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

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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}

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Now we proceed to calculate the percent error:

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(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:

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Now we proceed with the error for the circumference:

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