Numerade

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You place a crate of mass 32.8 kg on a frictionless 4.55-meter-long incline. You release the crate from rest, and it begins to slide down, eventually reaching the bottom 2.17 s after you released it. What is the angle of the incline?

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11. A 100 kg car accelerates uniformly from rest for a distance of 20 min 10 s. What is the car's momentum at time t = 5 s?

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The more inelastic the demand and the more inelastic the supply, the smaller the consumer surplus is relative to the producer surplus.

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In this relationship we find one organism is gaining no benefit but is also not being harmed while the other gains direct benefit.

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A consumer's preferences for goods X and Y are given by U(X, Y) = X^0.6Y^0.4. The price of X is $10, and the price of Y is $20. The consumer has an income of $5000. a. What is the utility-maximizing choice of X and Y? b. How would the utility-maximizing choice change if the price of Y increased to $50? c. Given the answers to the previous parts, plot a linear approximation to the demand function for Y.

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Evaluate the following. Given F=ma, find the value of m, when a=9 and F=72

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Texts: Ms. Lover Foolish is the CEO of a company producing a new magical supplement "Love is Strange". A marketing campaign promised an increase in intimacy as you use this new supplement. Ms. Foolish conducted a study to estimate the demand for "Love is Strange" and found the following: Let P(X) = price of Love is Strange; P(y) = the price of a cream: "Life is fun"; M = income, A = Advertising expense; Q = quantity demanded of "Love is Strange" P(x) P(y) M A Q 56.41 43.22 42.68 61.31 63.26 21.82 68.46 14.32 55.06 65.42 26.42 39.79 51.23 14.78 37.78 64.16 66.32 10.92 62.99 14.22 73.83 45.76 20.11 42.62 69.26 15.52 81.06 37.15 85.34 46.81 19.98 10.19 36.86 74.63 53.94 81.21 77.42 20.86 12.35 53.17 73.82 35.68 25.01 89.25 34.79 76.06 32.56 24.67 47.00 57.05 75.72 66.92 31.95 50.43 8.49 31.55 69.17 51.32 64.44 7.54 29.54 9.34 19.46 2.00 1 1- Assuming that the demand is not linear, use a log-linear estimation to find the log-linear demand function. 2- Is the cream "Life is fun" a substitute or a complementary good? Why? 3- Ms. Foolish claimed that the demand function should be linear. Use a linear estimation method to find the linear demand function. Would your findings support a linear function? Why? 4- Using the linear demand function you derived in part 3, if P(x) = 50, P(y) = 15, M = 1200, A = 518, find the cross-price elasticity E[Q(X), P(Y)].

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Problem 3: A Potpourri of Different Problems (a) Consider a delta-connected balanced source for which the voltage differences between the lines are given by Vab, Vbc, Vca that satisfy Vbc = Vab - j2n/3 and Vca = Vab + j2n/3. Find an equivalent wye-connected source with voltage differences Van, Von, Ven in terms of Vab, Voe, and Vea that satisfy Vab = Van - Von, Vbc = Von - Vcn, and Vca = Vcn - Van. (b) In this problem, we perform a sanity check on our voltage-current relationships across a transmission line. Consider a transmission line of length d1 + d2 as shown in Figure 1. Per our analysis in class, we have where the matrix T(d) is a 2x2 matrix for a given distance d and is given by cosh(d) Z sinh(d) cosh(d) The voltage-current relationships for the (d1 + d2) length transmission line must satisfy Prove that T(d + d) = T(d)T(d) for (6) and (8) to be consistent. A three-phase line, which has an impedance of (1 + j2) per phase, feeds two balanced three-phase loads that are connected in parallel. One of the loads is wye-connected with an impedance of (15 + j20) per phase, and the other is delta-connected with an impedance of (60 - j45) per phase. The line is energized at the sending end from a 60-Hz, three-phase, balanced voltage source of 120/âˆš3 V. Compute the current, real power, and reactive power delivered by the sending-end source. Find the line-to-line voltage at the load and the current per phase in each load. Calculate the total three-phase real and reactive powers absorbed by each load and report its magnitude in volt-amperes, whether it is leading or lagging, and the power factor.

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8. A mixture consists of 60 g of ice and 40 g of liquid water, both at 0°C. The amount of heat that must be added to melt all of the ice is about ($L_f$=80 cal/g) Show calculation: () 3200 cal () 4000 cal () 4800 cal () 8000 cal 9. An ice cube of mass 100 g and at 0°C is dropped into a Styrofoam cup containing 200 g of water at 25°C. Calculate how much heat is available by cooling the water to 0°C and how much heat is required to melt the ice. Available Heat: $Q_{available}$=____ cal. $L_f$=80 cal/g; $c_w$ = 1.0 cal/g °C Required heat: $Q_{required}$=____ cal Will all the ice melt?_____ Show calculation:

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1. a) Consider the vectors $\vec{u} = (-7, 4, -1)$ and $\vec{v} = (8, 0, -6)$ calculate $4\vec{u} - \frac{3}{2}\vec{v}$. [2] b) Express the result from a) in unit vector from (linear combination of $\vec{i}$, $\vec{j}$, and $\vec{k}$) [2] c) Determine the exact value of $|\vec{u} + \vec{v}|$. [2] 2. If $|\vec{a}| = 5$, $|\vec{b}| = 8$ and the angle between the two vectors is 120°, determine the unit vector in the same direction as $2\vec{a} - 3\vec{b}$. State the direction as an angle in relation to $\vec{a}$. [4]

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carla k.