Aparticle undergoes a displacement δr⃗ of magnitude 54 m in a direction 42 ∘ below the x axis. express δr⃗ in terms of the unit vectors x^ and y^.

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The ideal gas model is valid if which of the following conditions is true? the gas density is low. the gas density is high. the temperature is low. the temperature is high. the gas density and the temperature are low. the gas density and the temperature are high. the gas density is high and the temperature is low. the gas density is low and the temperature is high.

Adielectric-filled parallel-plate capacitor has plate area a = 30.0 cm2 , plate separation d = 9.00 mm and dielectric constant k = 3.00. the capacitor is connected to a battery that creates a constant voltage v = 15.0 v . throughout the problem, use ϵ0 = 8.85x10-12 c2/n.m2 . find the energy u1 of the dielectric-filled capacitor.