AFN equation

Broussard Skateboard's sales are expected to increase by 20% from $7.0 million in 2016 to $8.40 million in 2017. Its assets totaled $5 million at the end of 2016. Broussard is already at full capacity, so its assets must grow at the same rate as projected sales. At the end of 2016, current liabilities were $1.4 million, consisting of $450,000 of accounts payable, $500,000 of notes payable, and $450,000 of accruals. The after-tax profit margin is forecasted to be 4%, and the forecasted payout ratio is 55%. What would be the additional funds needed? Do not round intermediate calculations. Round your answer to the nearest dollar.
$

Assume that an otherwise identical firm had $6 million in total assets at the end of 2016. The identical firm's capital intensity ratio (A₀*/S₀) is -Select-higher than? lower than? equal to? than Broussard's; therefore, the identical firm is -Select-less? more? the same? capital intensive - it would require -Select-a smaller? a larger? the same? increase in total assets to support the increase in sales.

A toboggan with two people on it weighs 300 lb. It starts from rest down a slope, 1/4 mile long, from a height 200 ft above horizontal level. The coefficient of sliding friction is 3/100 and the force of the wind resistance is proportional to the square of the velocity. When the velocity is 30 ft/sec, this force is 6 lb.

(a) Find the velocity of the toboggan as a function of the distance and of the time.

(b) With what velocity will the toboggan reach the bottom of the slide?

(c) When will it reach the bottom?

(d) What would its terminal velocity be if the slide were infinite in length?

Answers:

(a) v= 74.1 (e^(0,105t)-1)/(e^(0.105t)+1), v^2=5484(1-e^(-0.0014s)

(b) 68 ft/sec

(c) 30 sec, approx.

(d) 74.1 ft/sec

I'm having trouble solving for v originally. Any help would be much appreciated.

A voltaic cell consists of a Pb/Pb2+ half-cell and a Cu/Cu2+ half-cell at 25 ∘C. The initial concentrations of Pb2+ and Cu2+ are 5.30×10⁻² M and 1.60 M , respectively.

Part A

What is the initial cell potential? Express your answer using two significant figures.

Ecell= ? V

Part B

What is the cell potential when the concentration of Cu2+ has fallen to 0.230 M ?

Express your answer using two significant figures.

Part B

What is the cell potential when the concentration of Cu2+ has fallen to 0.230 M ? Express your answer using two significant figures.

Ecell=? V

Part C

What are the concentrations of Pb2+ and Cu2+ when the cell potential falls to 0.360 V ? Enter your answers numerically separated by a comma. Express your answer using two significant figures.

[Pb2+],[Cu2+]= ? M

Cirrhosis Case Study Mr. V. is a 55-year-old alcoholic who checked into a clinic, complaining he has been experiencing a persistent cough and has been feeling more fatigued, nauseous, and irritable. In addition, he is experiencing more frequent memory lapses. His abdomen is distended, but on palpation, his liver is small in size and firm, indicating cirrhosis. Lab tests indicate a decrease in hemoglobin, albumin, and prothrombin levels with elevated serum bilirubin and ammonia levels

. Case Study Questions

1. Differentiate the various stages that Mr. V.’s liver has progressed through and the implications of the current stage.

2. Examine specific rationale for each of Mr. V.’s manifestations and blood values.

3. Appraise whether it is possible to reverse the damage to the liver at this stage. What is Mr. V's prognosis?

4. Evaluate significant complications that are likely to occur, include a discussion on predisposing factors and effects on the liver.

In this exercise, we will investigate the chemical potential μμ upon a change in volume. We will use the fact that F=U−TSF=U−TS and μ=∂F/∂N. We will compute μ(Vf)−μ(Vi)μ(Vf)−μ(Vi)

In all questions, take N=20 moles (which is 20 times Avagodro's number of particles), T=300 K, V_i=0.01 m³,V_f=0.02 m³

1) For a gas with an excluded volume:

• U=3/2NkT+const
• S=Nkln(V−bN)+const

If bb=10^-28 m³, compute μ(Vf)−μ(Vi)

2.) For a gas with an excluded volume and attraction between the particles:

• U=3/2NkT−aN^2/V+const
• S=Nkln(V−bN)+const

If aa=10^-49 m³ and bb=10^-28 m³, compute μ(Vf)−μ(Vi)

Two capacitors, C1 and C2, are connected in series and a battery, providing a voltage V, is connected across the two capacitors. (a) Find the equivalent capacitance, the energy stored in this equivalent capacitance, and the energy stored in each capacitor. (b) Show that the sum of the energy stored in each capacitor is the same as the energy stored in the equivalent capacitor. Will this equality always be true, or does it depend on the number of capacitors and their capacitances? (c) If the same two capacitors were connected in parallel, what potential difference would be required across them so that the combination stores the same energy as in the system of part (a)? Express everything in terms of the given quantities, C1, C2, and V. (d) If C1 =18μF,C2 = 36μF,V =12V, evaluate the equivalent capacitance and energy stored in the serial case of part (a), the equivalent capacitance and voltage of the parallel circuit of part (c). (e) In both cases, which capacitor stores more energy, C1 or C2?

1) Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by y=x^2, y=0, and x=5, about the y-axis.

V=

2) Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by y=x^2, y=0, and x=6, about the yy-axis.

V=

3)The region bounded by f(x)=−3x^2+15x+18f(x)=-3x2+15x+18, x=0x=0, and y=0y=0 is rotated about the y-axis. Find the volume of the solid of revolution.

Find the exact value; write answer without decimals.

4) Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on the right by the graph of g(y)=4/y and on the left by the y-axis for 1≤y≤11, about the x-axis. Round your answer to the nearest hundredth position.
V=

(i) Rank the following five capacitors from greatest to smallest capacitance, noting any cases of equality. (Use only ">" or "=" symbols. Do not include any parentheses around the letters or symbols.)

(a) a 20-µF capacitor with a 4-V potential difference between its plates
(b) a 30-µF capacitor with charges of magnitude 90 µC on each plate
(c) a capacitor with charges of magnitude 80 µC on its plates, differing by 2 V in potential
(d) a 10-µF capacitor storing energy 125 µJ
(e) a capacitor storing energy 250 µJ with a 10-V potential difference

(ii) Rank the same capacitors in part (i) from largest to smallest according to the potential difference between the plates.

(iii) Rank the capacitors in part (i) in the order of the magnitudes of the charges on their plates.

(iv) Rank the capacitors in part (i) in the order of the energy they store.

Please explain how you got your answer.

Question2.

Let A = [2 1 1

1 2 1

1 1 2 ].

(a) Find the characteristic polynomial PA(λ) of A and the eigenvalues of A. For convenience, as usual, enumerate the eigenvalues in decreasing order λ1 ≥ λ2 ≥ λ3.

(b) For each eigenvalue λ of A find a basis of the corresponding eigenspace V (λ). Determine (with a motivation) whether V (λ) is a line or a plane through the origin. If some of the spaces V (λ) is a plane find an equation of this plane.

(c) Find a basis of R 3 consisting of eigenvectors if such basis exist. (Explain why or why not). Is the matrix A diagonalizable? If ”yes”, then write down a diagonalizing matrix P, and a diagonal matrix Λ such that A = PΛP −1 , P −1AP = Λ. Explain why the matrix P is invertible but do not compute P −1 .

(d) Consider the eigenvalues λ1 > λ3. Is it true that the orthogonal complements of the eigenspaces satisfy (Vλ1 ) ⊥ = Vλ3 , (Vλ3 ) ⊥ = Vλ1 ? Why or why not??