solve the following in detailed 1. Consider the curve 3x + y -5xy = 2 and...

solve the following in detailed

1. Consider the curve 3x + y -5xy = 2 and find an expression for dy/dx

2. A 15 foot ladder is leaning against a wall. If the bottom of the ladder is sliding away from the wall at a rate of 1.5 feet/sec, how quickly is the top of the ladder moving down the wall when the bottom of the ladder is 5 feet from the wall?

Expert Solution

milcah answered 1 year ago

z=26x-3x^2+5xy-6y^2+12y subject to 3x+y=170 a- Find the critical values at which the following function will be...

z=26x-3x^2+5xy-6y^2+12y subject to 3x+y=170 a- Find the critical values at which the following function will be optimized subject to the given constraints. b- estimate the effect on the value of the objective function from a one unit change in the constant of the constraint.

2. For the curve y = 3x / x^2-1 determine each of the following and use...

2. For the curve y = 3x / x^2-1 determine each of the following and use all of the information to draw its graph and notate the information on it. (a) Find the domain of the function, as well as any x or y intercepts and symmetry. (b) Find all vertical (2 of them) and horizontal (1) asymptotes. Support your work with limits. (c) Use the first derivative to determine the maximums, minimums and intervals of increase/decrease of f(x). (d)...

Solve ODE (3x - 2y + 1)dx + (-2x + y + 2)dy = 0 with...

Solve ODE (3x - 2y + 1)dx + (-2x + y + 2)dy = 0 with the method of x =u + h and y = v + k

y'' + y=tanx+3x-1 solve the ode and find the general solution?

Solve the set of equations: 3x - 5y = - 1, x - y = - 1?

Solve the following initial value problem: y'''-4y''+20y'=-102e^3x, y(0)=3, y'(0)=-2, y''(0)=-2

Consider the following planes. 5x − 3y + z = 2, 3x + y − 5z...

Consider the following planes. 5x − 3y + z = 2, 3x + y − 5z = 4 (a) Find parametric equations for the line of intersection of the planes. (Use the parameter t.) (x(t), y(t), z(t)) = (b) Find the angle between the planes. (Round your answer to one decimal place.)

Solve the following DEs 1.) dy/dx + y =e^3x 2.) x^2y' +xy = 1 3,) x(dy/dx)-y...

Solve the following DEs 1.) dy/dx + y =e^3x 2.) x^2y' +xy = 1 3,) x(dy/dx)-y = x^2 sin(x) 4.) y' - 2y = e^2x, y(0) = 2 5.) cos(x)(dy/dx) + ysin(x) = 1, y(pi/4) = 0

Solve (1+e^x)dy/dx+(e^x)y=3x^2+1 Solve (x^3+y^3)dx+3xy^2 dy = 0 Solve (y-cos y)dx + (xsiny+x)dy = 0 Solve (1+ln...

Solve (1+e^x)dy/dx+(e^x)y=3x^2+1 Solve (x^3+y^3)dx+3xy^2 dy = 0 Solve (y-cos y)dx + (xsiny+x)dy = 0 Solve (1+ln x +y/x)dx = (1-lnx)dy Solve (y^2+yx)dx - x^2dy =0 Solve (x^2+2y^2)dx = xydy Solve Bernoulli's Equation x dy/dx + 2y = (x^4)(e^x)(y^2) Solve Bernoulli's Equation (1+x^2) dy/dx = 2xy +(e^x)(y^2) Solve IVP (3e^(x^2))dy + (xy^2)dx=0 ; y(1) = 2 Solve IVP dy/dx -2xy = e^(x^2) ; y(0)=0 Solve IVP (x^2+y^2)dx+(2xy)dy=0; y(1)=1 6. Mixture Problem Initially 40 lb of salt is dissolved in a large...

Solve a. x + y = 3, 2x – y = 1 b. 3x + 2y = 6,...

Solve a. x + y = 3, 2x – y = 1 b. 3x + 2y = 6, x = 3 c. 2x + y = 4, y = -2x + 1 d. x – 3y = 6, 2x – y =1

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