Respuesta :

jbmow
The diagonal of a square is equal to the side x times square root of 2, xSqrt(2)
z = xSqrt(2), its rate of change is just Sqrt(2)
fichoh

The rate of change of Area, A with respect to the diagonal length, z and the rate of change when z = 2 is :

  • [tex]\frac{dA}{dz} = z [/tex]

  • [tex]\frac{dA}{dz} = 2 \: when \: z = 2 [/tex]

The area of a square is rated to its diagonal thus :

  • Area of square = A

  • Length of diagonal = z

The relationship between Area and diagonal of a square is : [tex]A \: = 0.5 {z}^{2} [/tex]

The rate of change of area with respect to the length, z of the square's diagonal ;

This the first differential of Area with respect to z

[tex] \frac{dA}{dz} = 2(0.5)z \: = z[/tex]

Therefore, the rate of change of area, A with respect to the length, z of the diagonal is [tex]\frac{dA}{dz} = z [/tex]

The rate of change [tex]\frac{dA}{dz} [/tex] when z = 2 can be calculated thus :

Substitute z = 2 in the relation [tex]\frac{dA}{dz} = z [/tex]

Therefore, [tex]\frac{dA}{dz} = 2 [/tex]

Learn more :https://brainly.com/question/3122130?referrer=searchResults

Otras preguntas