The voltage pulse described by the following equations is impressed across the terminals of a 0.5µF capacitor. v(t) = 0 t ≤ 0 v(t) = 4t V 0 ≤ t ≤ 1 v(t) = 4e-(t-1) V 1 ≤ t ≤ [infinity] a. Derive the expressions for the capacitor current, power, and energy. b. Sketch the voltage, current, power, and energy as functions of time. Line the plots up vertically so that for a given time interval the behavior of each variable can easily be assessed. c. Specify the interval of time when energy is being stored in the capacitor. d. Evaluate the integral ∫ from (i) t = 0 to 1 and (ii) t = 1 to [infinity]; comment on the significance of these two integrals

Stu and ambrose are working together on a study of whether diet is related to students' mental health. first, they randomly select 10 students from the student center and 10 students from the office of counseling and psychological services. then, they ask students to rate their diet in terms of healthiness on a scale of 1-100 before completing a 20-item mental health survey. a) name one of the constructs being studied b) how was the construct you named above operationally defined in this experiment? e) was the variable you described above their independent variable, their dependent variable, or a controlled variable? d) what is a confounding variable? what is a potential confound in this study?