See attached Determine a vector equation...for the line that passes through the point P(1, 2, 3) and is perpendicular to the plane 4x+5y+6z=7. Consider the planes...If these planes are parallel, determine their distance. Otherwise determine their angle of intersection.
See attached Dot and cross product (3P+3P+2P) Determine all values ...such that the vectors...are orthogonal. Determine a unit vector...that is orthogonal to both...
Please show all steps to solution. Consider the first-order linear differential equation (see attached) (a) Determine the general solution to the initial-value problem(*) with y(1) =0 (b)Find three initial-conditions y(a) = b,for which the initial-value problem has no solution and a
Please show all steps to solution. Find three points (a,b) in the plane for which the initial-value problem dy/dx= √(1-y^2 ) y(a) = b has a unique solution,no solution and an infinite number of solutions,r
Please show all steps to solution. A tank with a capacity of 500 gal originally contains 200 gal of water with 100 lb of salt in solution. Water containing a salt concentration of 1 lb/gal enters the tank at a rate of 3 gal/min, and the mixture is allowed to flow out of the tank at the rate of 2 gal/min. (a) Find the amount
Separating Variables - The problem is: dP/dt = P - P^2 The given answer is: P = ce^t/1+ce^t How do I get to the final answer?
Separation of Variables - The problem is: dS/dr = kS The given answer is: S = ce^kr Will you explain to me how this answer was obtained?
Solve the differential equation (e^y + 1)^2 e^-y dx + (e^x + 1)^3 e^-x dy = 0
Solve the differential equation by method of separation of variables csc y dx + sec^2 x dy = 0 I have to use separation of variables to solve this problem. The answer given is: 4 cos y = 2x + sin 2x + C I've worked on this problem for quite a while and cannot come up with the given answer.
Fran throws a rock straight upward alongside a tree. The rock rises until it is even with the top of the tree and then falls back to the ground; it remains aloft for 4 s. How tall is the tree? The tree is 64 ft tall.
Solve the equation: 10^(x+2)=5e^(6-x)
Ropes 3 m and 5 m in length are fastened to a holiday decoration that is suspended over a town square. The decoration has a mass of 5 kg. The ropes, fastened at different heights, make angles of 52 degrees and 40 degrees with the horizontal. Find the tension in each wire and the magnitude of each tension.
Describe in words the region of R^3 represented by the equation. 1.) xy=0 2.) xyz=0
I must verify that the indicated expression is an IMPLICIT solution to the given first-order differential equation. dX/dt = (X - 1)(1 - 2X); ln(2X - 1)/(x - 1) = t
Multiple choice questions for Laplace Transform problems. Please answer and give detailed solution to better understand material See attached
Please help me understand these problems. State the Comparison Test, the Limit Comparison Test and the Integral Test for the convergence of infinite series.
Find the slope and the y- intercept of the following line 7y-8x-2=0
Please show in detail how to solve the series. Thank you. Does converge or diverge?
See attachment for equations
How to Evaluate Functions Evaluate the functions for the values of x given as 1, 2, 4, 8, and 16. Describe the differences in the rate at which each function changes with increasing values of x. 1. f(x) = 5x - 3 2. f(x) = x2 - 3x + 2 3. f(x) = 2x3 + 7x2 - x - 1 4. f(x) = 10x 5. f(x) = ln x
Please show all work. Thanks
See attached Find a linear differential equation whose general solution is... Find an explicit form of the general solution to the equation...
Question on Stochastic Differential Equations. Show that G=exp(t+aexp(X(t))) is a solution of the stochastic differential equation... Stochastic Calculus (a) Show that Is a solution of the stochastic differential equation (b) By considering the form show that where should be determined. Similar form que
Geometric series and limits. Please see attached.
Find the general solution of the given differential equation: (4-x)dy+2ydx=0 Find the solution to the initial-valued problem (x^2+1)Y'=xe^y with initial condition y(0)=?
Using 1. f(x) = , find f'(x) and then add the tangent line to the graph of y=f(x) at x = 0 2. f(x) = , find f'(x) [See attachment for equations.]
A new bridge is to be constructed over a big river. The space between the supports must be 1000 feet; the height at the center of the arch needs to be 320 feet. The support could be in the shape of a parabola or a semi-ellipse. An empty tanker needs a 250 foot clearance to pass beneath the bridge. The width of the channel for ea
Total cost of producing goods. See attached for full description. 4. The total cost of producing q units of product is given by C(q) = q^3 - 60q^2 +1400q + 1000 for 0 < q <= 50; the product sells for $788 per unit. What production level maximizes profit? Find the total cost, total revenue, and total profit at this production
#5 Let p(x) = x3 -ax, where a is constant a) If a<0, show that p(x) is always increasing. substituting in values b) If a>0, show that p(x) has a local maximum and a local minimum. c) Sketch and label typical graphs for the cases when a<0 and when a>0. Find the value(s) of x for which: a) f(x) has a local maximum
#4 What happens to concavity when functions are added? a) If f(x) and g(x) are concave up for all x, is f(x) + g(x) concave up for all x? Yes b) If f(x) is concave up for all x and g(x) is concave down for all x, what can you say about the concavity of f(x) + g(x)? For example, what happens if f(x) and g(x) are both polyn