a film of transparent material 120 nm thick and having refractive index 1.25 is placed on a glass sheet having refractive index

Answer:

a)  τ = i ^ (y - z ) + j ^ (z Fₓ - x ) + k ^ (x - y Fₓ)

b) τ = (-0.189i ^ -5.6 j ^ + 33.978k ^) N m

c) α = (-7.8 10⁻⁴ i ^ - 2.3 10⁻² j ^ + 1.4 10⁻¹ k ^) rad / s²

Explanation:

a) The torque can be expressed as

        τ = r x F

To tackle this equation, using the determinant approach is the most straightforward method

The resulting expression is

      τ = i ^ (y - z ) + j ^ (z Fₓ - x ) + k ^ (x - y Fₓ)

b) Now let's compute

     τ = i ^ (0.075 1.4 -0.035 8.4) + j ^ (0.035 2.8 - 4.07 1.4) + k ^ (4.07 8.4 - 0.075 2.8)

     τ = i ^ (- 0.189) + j ^ (-5.6) + k ^ (33,978)

     τ = (-0.189i ^ -5.6 j ^ + 33.978k ^) N m

c) To find angular acceleration, we use

       τ = I α

       α = τ / I

The moment of inertia being a scalar means that only the magnitude of each component changes, orientation remains constant.

     α = (-0.189i^  -5.6 j^  + 33.978k^) / 241

     α = (-7.8 10⁻⁴ i ^ - 2.3 10⁻² j ^ + 1.4 10⁻¹ k ^) rad / s²

Answer: Known facts are:

Sadie, the dam, is a black Labrador.

Sam, the potential sire, is a yellow Labrador.

Putting aside technical methods, the breeder can inspect the puppies for traits.

For instance, yellow coat color is recessive to black, so yellow pups would suggest Sam is likely the father; however black pups could also have Sam as sire if they inherited the mother's color alleles.

Examining coat color, conformation, and similar features is a reasonable starting point.

Ultimately these observations are probabilistic; the only definitive (scientific) method is a paternity (DNA) test.

Answer:

The properties of ligand-gated ion channels include:

a. They play a crucial role in the nervous system by altering sodium and calcium levels within cells.  

b. Their significance is primarily linked to the nervous system.

c. They are vital for the nervous system, responsible for modulating sodium and calcium levels in cells, and they respond to chemical signals by either opening or closing.

Explanation:

Ligand-gated ion channels (LICs or LGICs), often called ionotropic receptors, represent a class of trans-membrane ion-channel proteins that open to permit the flow of ions like Na+, K+, Ca2+, and/or Cl− across membranes in reaction to the binding of chemical signals. Their function contrasts with that of voltage-gated ion channels, which are triggered by changes in voltage across membranes (i.e., when depolarization occurs) and are responsive to membrane potentials. In comparison to GPCRs that utilize secondary messengers, ligand-gated channels operate upon the binding of a ligand (a specific chemical signal). Both types of channels are essential for the effective activation of the post-synaptic neuron.