Question Solved1 Answer Mountain Mack spends his time carving fishing lures and duck decoys. If Mountain Mack spends all of his time carving fishing lures he can carve 20 lures in a week. If he spends all of his time carving duck decoys he can carve 40 decoys in a week. For every 8 duck decoys Mountain Mack carves he must give up 4 fishing lures. Mountain Mack spends his time carving fishing lures and duck decoys. If Mountain Mack spends all of his time carving fishing lures he can carve 20 lures in a week. If he spends all of his time carving duck decoys he can carve 40 decoys in a week. For every 8 duck decoys Mountain Mack carves he must give up 4 fishing lures. Mountain Mack's Production Possibilities Schedule Fishing Lures Duck Decoys 20 40 Instructions: Enter your answers as a whole number. Fill in the values in the table to complete Mountain Mack's production possibilities schedule.

Consider the diagram to the right, which applies to a nation with no government spending, taxes, and net exports. Use the information in the diagram to answer the following questions. The marginal propensity to save for this economy is .25 Planned C, 1 147 13- 12- 11- F 10- 9-1 The present level of planned investment spending for the present period is $ trillion. The equilibrium level of real GDP for the present period is trillion. 8- 7- G $ 6- 5- 3- 2 The equilibrium level of saving for the present period is $ trillion. If planned investment spending for the present period increases by $25 billion, the resulting change in equilibrium real GDP will be $ trillion. If other things, including the price level, remain unchanged, the new equilibrium level of real GDP will be $1 trillion. 1- Y 0 1 2 4 5 6 7 8 9 10 11 12 13 14 Real GDP ($ trillions)

Consider the figure below. (Due to the nature of this problem, do not use rounded intermediate values in your calculations—including answers submitted in WebAssign.) (a) Find the charge stored on each capacitor in the figure shown above (C1 = 10.2 µF, C2 = 8.80 µF) when a 1.71 V battery is connected to the combination. Q1 = C Q2 = C Q3 = C (b) What energy is stored in each capacitor? E1 = J E2 = J E3 = J Consider the figure below. (Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) 0.300F (a) Find the charge stored on each capacitor in the figure shown above (C1 = 10.2 pF, C2 = 8.80 PF) when a 1.71 V battery is connected to the combination Q1 = с Q2 с Q3 (b) What energy is stored in each capacitor? EL E2 Ez = Additional Materials Reading

(figure 1) shows an acceleration-versus-force graph for three objects pulled by identical rubber bands. The mass of object 2 is 0.10 kg Figure 1 of 1 a (m/s) 1 5- 2 4 3 3 1 0 0 1 2 3 4 5 6 Force (number of rubber bands)

A planet of mass 4 ⨯ 1024 kg is at location 5 ⨯ 1011, −4 ⨯ 1011, 0 m. A star of mass 4 ⨯ 1030 kg is at location −6 ⨯ 1011, 5 ⨯ 1011, 0 m. It will be useful to draw a diagram of the situation, including the relevant vectors. (a) What is the relative position vector r pointing from the planet to the star? r = 〈−11·1011, 9·1011, 0〉 m (b) What is the distance between the planet and the star? |r| = m (c) What is the unit vector in the direction of r? = 〈−.774, .633, 0 〉 (d) What is the magnitude of the force exerted on the planet by the star? |Fon planet| = N (e) What is the magnitude of the force exerted on the star by the planet? |Fon star| = N (f) What is the force (vector) exerted on the planet by the star? (Note the change in units.) Fon planet = 〈−3.35, 4.09, 0〉 ⨯ 1020 N (g) What is the force (vector) exerted on the star by the planet? (Note the change in units.) Fon star = ⨯ 1020 N

Plot a, (Stewart 9.3 30 and 34, modified) Let a = (1, 2) and b = (-4,1). (a) Find the vector projection of b onto a, denoted projab and find its length (called the scalar projection). b and projab in the plane. (b) The orthogonal projection of b onto a, denoted orthab is the vector b - projab. Find orthab and plot it in the plane. Why do you think we call orthab the orthogonal projection of b onto a? What vector(s) is it perpendicular to in the example you sketched? (c) Show for any non-zero vectors a and b that orthab is perpendicular to a.

(a) Use the definition given below with right endpoints to express the area under the curve y = x3 from 0 to 1 as a limit. = The area A of the region S that is bounded above by the graph of a continuous function y = f(x), below by the x-axis, and on the sides by the lines x = a and x = b is the limit of the sum of the areas of approximating rectangles. n lim Rn A = n00 lim [f(x4)Ax + f(x2)4x + = + f(x,)Ax] = lim. į f(x;)Ax n00 i=1 n lim n00 i = 1 (b) Use the following formula for the sum of cubes of the first n integers to evaluate the limit in part (a). 12 13 + 23 + 33 + ..-( ) 3 = n(n + 1) 2