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Differential Equations
Consider the equation yu_x - xu_y = 0, (y>0). Check for each of the following initial conditions whether the problem is solvable. If it is solvable, find a solution. If it is not, explain why:
a) u(x,0) = x^2
b) u(x,0) = x
c) u(x,0) = x, x>0
a) u(x,0) = x^2
b) u(x,0) = x
c) u(x,0) = x, x>0
Differential Equations
Which of the following statements is CORRECT?
a. When calculating the cost of preferred stock, a company needs to adjust for taxes, because
preferred stock dividends are deductible by the paying corporation.
b. All else equal, an increase in a company’s stock price will increase its marginal cost of
retained earnings, rs.
c. All else equal, an increase in a company’s stock price will increase its marginal cost of new
common equity, re.
d. Since the money is readily available, the after-tax cost of retained earnings is usually much
lower than the after-tax cost of debt.
e. If a company’s tax rate increases but the YTM on its noncallable bonds remains the same,
the after-tax cost of its debt will fall.
a. When calculating the cost of preferred stock, a company needs to adjust for taxes, because
preferred stock dividends are deductible by the paying corporation.
b. All else equal, an increase in a company’s stock price will increase its marginal cost of
retained earnings, rs.
c. All else equal, an increase in a company’s stock price will increase its marginal cost of new
common equity, re.
d. Since the money is readily available, the after-tax cost of retained earnings is usually much
lower than the after-tax cost of debt.
e. If a company’s tax rate increases but the YTM on its noncallable bonds remains the same,
the after-tax cost of its debt will fall.
Differential Equations
Solve the equation xu_x + (x+y)u_y = 1 with the initial condition u(1,y) = y. Is the solution defined everywhere?
Differential Equations
Prove that the system:
U_x = 2.999999x^2y + y
U_y = x^3 + x
has no solution at all.
U_x = 2.999999x^2y + y
U_y = x^3 + x
has no solution at all.
Differential Equations
Solve the equation xu_x + (x+y)u_y = 1. with the initial condition u(1,y) = y. Is the solution defined everywhere?
Differential Equations
Show that there exists a unique solution for the system:
U_x = 3x^2y+y
U_y = x^3+x
together with the initial condition u(0,0) = 0.
U_x = 3x^2y+y
U_y = x^3+x
together with the initial condition u(0,0) = 0.
Differential Equations
Consider the equation yu_x - xu_y = 0 (y>0). Check for each of the following initial conditions whether the problem is solvable. If it is solvable, find a solution. If it is not, explain why:
(a) u(x,0) = x^2
(b) u(x,0) = x
(c) u(x,0) = x, x>0
(a) u(x,0) = x^2
(b) u(x,0) = x
(c) u(x,0) = x, x>0
Differential Equations
Show that each of the following equations has a solution of the form u(x,y) = e^(ax+by). Find the constants a,b for each example:
a) u_x + 3u_y + u = 0.
b) u_xx + u_yy = 5e^(x-2y).
a) u_x + 3u_y + u = 0.
b) u_xx + u_yy = 5e^(x-2y).
Differential Equations
If my work says use cross products to solve each proportion what I'm susposed to do?
Differential Equations
What if Jason had a total of 5 cranks that could take baskets to the ground. Crank 4 moved at a rate of every three cranks the basket moved 3 feet and Crank 5 moved at a rate of every 1 crack it noved 5 feet. Which basket would reach the ground quicker?
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#339914 on Dec 2023
#339914 on Dec 2023