The Gaia satellite will measure parallaxes with an accuracy of 2 × 10⁻⁵ arcsec for stars with V < 15.
(a) What is the distance d of an M5 I supergiant with log(L/L_ʘ) = 5.50 and BC = −3.70 that has V = 12, if the effect of interstellar extinction is ignored?
(b) What is the relative distance accuracy σ(d)/d of such a star?
(c) Assuming that T_eff is known, what is the relative accuracy in radius σ(R)/R?

A spherical capacitor has vacuum between its conducting shells and a capacitance of 125 pF. The outer shell has inner radius 9.00 cm.

a. If the potential of the inner shell is 355 V higher than the potential of the outer shell, what is the surface charge density on the outer shell?

b. If the potential of the inner shell is 355 V higher than the potential of the outer shell, what is the surface charge density on the inner shell?

Consider a myelinated nerve with axon of radius, a = 10 micrometers, and Myelin sheath of thickness b = 0.4a. A) Calculate the space constant. B) Assume that a potential change of ∆V = 10mV is required to initiate an action potential, and that the distance between two nodes of Ranvier is D = 200a. If the maximum potential change is ∆V = 100mV, how many nodes of Ranvier can be triggered

the specific values are right in the question if you actually read it

Starting with the exact differential for S (entropy, treated as a state function of P, pressure, and T, temperature), the definition of entropy, S, definition of heat, q, and the definition of enthalpy, H, show that

dS= (Cp/T)dT - alpha*V*dP

where

alpha= (1/V)*(dV/dT) when P is held constant

.Using the Helmholtz free energy, A, given by

A=U - TS

express dS in terms of dT and dV

1a) If the ventilation/perfusion ( V/Q) ratio of a lung region decreases, how will the P_O2 and P_CO2 in the blood in that region change?

1b) In perfusion-limited O₂ exchange, is the P_O2 at the end of the pulmonary capillary closer to P_A,O2 or P_V,O2?

1c) Which of the following is/are higher at the base of the lung than at the apex: blood flow, V/Q, ventilation, P_O2, P_CO2?

Please explain your answers briefly and accurately.

Use the following pair of reduction half-reactions to design a galvanic cell. Then write in the proper coefficient for each of the species involved in the overall reaction. Water molecules and protons are not shown in the half-reactions, but may be needed in the overall reaction.

MnO4- (aq) ? MnO2 (s) ?o = 0.59 V NO3- (aq) ? NO (g) ?o = 0.96 V

NO₃^- (aq)
MnO₄^- (aq)
NO (g)
MnO₂ (s)
H⁺ (aq)
H₂O (l)

Let X1,…,Xn∼i.i.d.N(0,σ2), for some σ2>0. Let σ2ˆ=1n∑i=1nX2i,andσ2˜=1n∑i=1n(Xi−Xnbar)2. Argue that both proposed estimators σ2ˆ and σ2˜ below are consistent and asymptotically normal. Then, give their asymptotic variances V(σ2ˆ) and V(σ2˜) and decide if one of them is always bigger than the other. Hint: Use the multivariate Delta method.

A homemade capacitor is assembled by placing two 9-in. pie pans 4cm apart and connecting them to the opposite terminals of a 6-Vbattery.

Part A:

Estimate the capacitance.

C= ?? V

Part B:

Estimate the charge on each plate.

Q= ?? C

Part C:

Estimate the electric field halfway between the plates.

E = V/m

Part D:

Estimate the work done by the battery to charge the plates.

W= ?? J

The force constants for the diatomic molecules CO and HI are 1860 N/m and 320 N/m respectively.

Plot the potential energy curves for these two in a way that highlights their differences (i.e. on a single graph).

Calculate the frequency of motion for both molecules (does this result surprise you?).

Calculate the wavelength of light needed to excite these molecules from their vibrational ground states (v=0) to their vibrational first excited states (v=1).