Numerade

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4. Determine the Fourier series for $f(t) = 2 \sin(3t) + 2 \sin(4t)$. (Hint use trigonometric representation) Find 5. Given the complex power delivered to an element if $V(\omega)$ is $V(\omega) = 4.2 \angle -21^\circ$ and the element impedance is given by $2+j2$. Find the current supplied to the element. If the voltage is Find S, P, Q also. $2+j2$ $V(\omega)$

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A tendency toward anger may be both physiological and related to family background. a learned response to over-protective parenting. simply a mood that will pass. a trait of emotionally mature people.

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Factor each trinomial: 33v^(2)-18v+2

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Determine the concentration of a solution prepared by diluting 25.0 mL of a stock 0.188 M Ca(NO3)2 solution to 150.0 mL. 25) A) 0.0501 M B) 1.13 M C) 0.0887 M D) 0.0313 M E) 0.0199 M

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Name the following organic compounds: CH? CH? CH?—CH—CH—CH?—CH—CH? ? CH? CH? CH? ? CH?—C—CH? ? CH? CH? CH? CH?—C—CH?—C—CH? ? CH? CH? 0 0 0

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The rescue effect __________________________________. (a) is intrinsic in all metapopulations especially when there is little heterogeneity (e.g., difference in resource availability) among patches or subpopulations (b) was demonstrated for tide pool sculpins along the Washington shoreline (c) is one way populations are able to survive in suboptimal habitats (d) only occurs at extinction rates below 50%

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The Enlightenment Question 18 options: Reinforced religious doctrine and metaphysics in resistance to modern trends of secularism Substituted reason for doctrine, agency for fatalism, independence for obedience, scientific method for superstition, and attention to self-agency over ideas of predestination Understood that the events of history were not chance occurrences but events that served to carry out a divine plan. Led to the idea that life, politics, economics, and society are about self-seeking, personal interest satisfaction, and the idea that such behavior will necessarily redound to the public good B & D

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(4 p.) Janice is planning to buy a 5% $80000 5-year bond. She is going to receive a quarterly dividend for 5 years. Which one of the following value is closest to the maximum amount she should pay today to make a nominal 12% per year compounded semiannually in this investment? (Assume no inter-period interest accrued when payment period is smaller than compounding period.) Select one: a. 59172 b. 66400 c. 80000 d. 59392

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5.9 This exercise relates $L^2(\mathbb{R})$ and $L^1(\mathbb{R})$. (i) Show that $L^1(\mathbb{R})$ is not a subspace of $L^2(\mathbb{R})$ (Hint: find a concrete function belonging to $L^1(\mathbb{R})$ but not to $L^2(\mathbb{R})$). (ii) Show that $L^2(\mathbb{R})$ is not a subspace of $L^1(\mathbb{R})$ (Hint: find a concrete function belonging to $L^2(\mathbb{R})$ but not to $L^1(\mathbb{R})$). (iii) Assume that $f \in L^2(\mathbb{R})$ has compact support. Show that $f \in L^1(\mathbb{R})$; in particular, this shows that $L^2(\mathbb{R}) \cap C_c(\mathbb{R}) \subset L^1(\mathbb{R})$.

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Answer All Questions Section A (3 points each) 1) The equation, $p_1A_1v_1 = p_2A_2v_2$ expresses the: a) conservation of mass b) conservation of momentum c) conservation of energy d) none of these 2) Water with a density of 1000 kg/m³ flowing through a pipe at 188.52 kg/s at an average velocity of 6 m/s has a volume flow rate of: a) 0.151 m³/s b) 157.10 kg/s c) 0.189 m³/s d) 15.36 m³/s e) none of these. 3) In the general energy equation studied in class, the term $h_a$ is often referred to as a) head losses due to friction b) head removed from the fluid c) total head on a pump d) total head of the fluid e) none of these 4) The equation $H = p/\gamma + v^2/2g + z$ accounts for the total ______ of the fluid at any section of the flow. a) Energy per unit weight b) momentum per unit mass, c) Total volume per unit mass d) none of these 5) The flow through a pipe has the following parameters: velocity of 3.6m/s, diameter of 0.15 m, density of 1258 kg/m³ and dynamic viscosity of 0.96 Pa.s. This flow is: a) laminar b) turbulent c) transitional d) none of these 6) The expression $h_L = f(Lv^2/2gD)$ can be used for a) only laminar flow b) only turbulent flow c) both laminar and turbulent flows d) none of these. 7) A body in a fluid whether floating or submerged is buoyed up by a force equal to the weight of the fluid displaced. This statement is known as a) Pascal's law b) Archimedes' principle, c) Bernoulli's law d) none of these 8) The Moody diagram can be used for a) only laminar flow b) only turbulent flow c) both laminar and turbulent flows d) none of these.

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kathryn r.