michaeltheballer1

michaeltheballer1

23.10.2020 •

Mathematics

10. The weight, in newtons, of an object in a particular location is equal to its mass, in kilograms, times the gravitational acceleration in that location. As a formula, this is
written w = mg, where w = weight, m = mass, and g = gravitational acceleration.
a. Neil Armstrong had a mass of 80 kg on Earth. On Earth's surface, the gravitational
acceleration is g = 10 newtons per kilogram. What was Niel's weight on Earth?
b. Rewrite the equation to isolate g
c. On the surface of the moon, Neil Armstrong's weight is 128 newtons. What is the
gravitational acceleration on the moon?newtons per kilogram.

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Ответ:

itsyagirlgona21

26.09.2020

(a)

$Maximum\ Error = 27$

$Relative\ Error = 0.008$

$Percentage\ Error = 0.8\%$

(b)

$Maximum\ Error = 36$

$Relative\ Error = 0.0267$

$Percentage\ Error = 2.67\%$

Step-by-step explanation:

Given

x = 15 -- edge length

$\triangle x = 0.2$ -- possible error

Solving (a): Errors in volume

The volume of a cube is:

V(x) = x^3

Differentiate

$\frac{dV}{dx} = 3x^2$

Make dV the subject

dV =3x^2dx

Rewrite as:

$\triangle V = 3x^2 \triangle x$

Substitute values for x and $\triangle x$

$\triangle V = 3 * 15^2 * 0.2^2$

$\triangle V = 27$

Hence:

$Maximum\ Error = 27$

The relative error is then calculated as:

$Relative\ Error = \frac{Maximum\ Error}{Volume}$

$Relative\ Error = \frac{27}{x^3}$

$Relative\ Error = \frac{27}{15^3}$

$Relative\ Error = \frac{27}{3375}$

$Relative\ Error = 0.008$

The percentage error is:

$Percentage\ Error = Relative\ Error * 100\%$

$Percentage\ Error = 0.008 * 100\%$

$Percentage\ Error = 0.8\%$

Solving (a): Errors in Surface Area

The volume of a cube is:

A(x) =6x^2

Differentiate

$\frac{dA}{dx} =12x$

Make dA the subject

dA = 12xdx

Rewrite as:

$\triangle A =12x\triangle x$

Substitute values for x and $\triangle x$

$\triangle A =12 *15 * 0.2$

$\triangle A =36$

Hence:

$Maximum\ Error = 36$

The relative error is then calculated as:

$Relative\ Error = \frac{Maximum\ Error}{Surface\ Area}$

$Relative\ Error = \frac{36}{6x^2}$

$Relative\ Error = \frac{36}{6*15^2}$

$Relative\ Error = \frac{36}{1350}$

$Relative\ Error = 0.0267$

The percentage error is:

$Percentage\ Error = Relative\ Error * 100\%$

$Percentage\ Error = 0.0267* 100\%$

$Percentage\ Error = 2.67\%$

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