Mathematics, 10.06.2020 15:57 lex1kkkk

The radius of a circular disk is given as 21 cm with a maximum error in measurement of 0.2 cm. A) Use differentials to estimate the maximum error in the calculated area of the disk.
B) What is the relative error?
C) What is the percentage error?

Answers: 2

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Answer from: jamarcuswilliam2515

a) $\Delta A \approx 26.389\,cm^{2}$ , b) $r_{A} \approx 0.019$ , c) $\delta = 1.9\,\%$

Step-by-step explanation:

a) The area of the circular disk is modelled after this expression:

$A = \pi \cdot r^{2}$

The total differential is given by the following formula:

$\Delta A = 2\pi r \cdot \Delta r$

The maximum absolute error in the calculated area of the disk is:

$\Delta A = 2\pi \cdot (21\,cm)\cdot (0.2\,cm)$

$\Delta A \approx 26.389\,cm^{2}$

b) The relative error is given by:

$r_{A} = \frac{\Delta A}{A}$

$r_{A} = \frac{26.389\,cm^{2}}{\pi \cdot (21\,cm)^{2}}$

$r_{A} \approx 0.019$

c) The percentage error is:

$\delta = r_{A}\times 100\,\%$

$\delta = 0.019 \times 100\,\%$

$\delta = 1.9\,\%$

Answer from: Quest

won't that be plagrisim thought?

step-by-step explanation:

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.