contestada

The side of a square floor tile is measured to be 28 inches, with a possible error of 1/32 inch. Use differentials to approximate the possible propagated error in computing the area of the square.

Respuesta :

Luv2Teach

Answer:

Step-by-step explanation:

The formula for the area of a square is

[tex]A=s^2[/tex]

We have a measured side to be 28 inches with an error of

[tex]-\frac{1}{32}\leq  ds\leq \frac{1}{32}[/tex]

To find the propogated error we need solve the differential equation for the change in the area, which is

dA = 2s*ds

dA = 2(28)(±1/32) which gives us

dA = ±1.75 inches squared

fichoh

The possible error in the area value of the square using differentials is ±1.75 inches

Given the Parameters :

  • Side length of square , [tex] s = 28 \: inches [/tex]
  • Possible error in measurement, [tex]ds = \frac{1}{32} [/tex]

Recall, the Formula for Area of a square :

  • [tex] Area \: of \: a \: square\:, A = s²[/tex]

To obtain the approximate possible error, [tex]dA[/tex], take the first derivative of Area :

  • [tex] \frac{dA}{ds} = 2s[/tex]

  • [tex] dA = (2s)(ds)[/tex]

Substitute the value of [tex] s[/tex] and [tex] ds [/tex] into the equation :

  • [tex] dA= 2 \times 28 \times \frac{1}{32} = 1.75 [/tex]

Therefore the possible error in the computed area value is ±1.75

Learn more :https://brainly.com/question/19573890

Otras preguntas