investigation (Diagonals in a Rectangle)

Diagonals in a Rectangle. In the case of a 2 X 2 rectangle, or a 3 X 5 rectangle, we can simply count. However, can we make a decision about a 100 X 167 or a 3600 X 288 rectangle? In general, given an N X K rectangle, how many grid squares are crossed by its diagonal?

calculus 3 and 4

Show all work, don't explain each step. Please DON'T submit answers back to me as an attachment. Thank you. Find the order of the differential equation and determine whether it is linear or nonlinear: y^(4) + 3(cos x)y''' + y'=0

calculus 3 and 4

Show all work, don't explain each step. Please DON'T submit answers back to me as an attachment. Thank you. Solve the initial value problem; it is not necessary to find all solutions of the equation: xy'=y(y-2), y(3)=2

Calculus 3 and 4

Show all work. Please DON'T submit answers back to me as an attachment. Thank you. Determine whether the function is homogenous. If it is, state the degree: f(x, y)=5x^2 + 2xy

calculus 3 and 4

Show all work, don't explain each step. Please DON'T submit answers back to me as an attachment. Thank you. State if the equation is seperable or homogenous: (x^2 + y^2) (dy/dx) = 5xy

calculus 3 and 4

Show all work, don't explain each step. Please DON'T submit answers back to me as an attachment. Thank you. State if the equation is seperable or homogenous: 2xy(dy/dx)=3

calculus 3 and 4

Show all work, don't explain each step. Please DON'T submit answers back to me as an attachment. Thank you. Find the general solution, if possible. Otherwise find a relation that defines the solutions implicitly: xy' - y=2y(ln y - ln x)

calculus 3 and 4

Show all work, don't explain each step. Please DON'T submit answers back to me as an attachment. Thank you. Find the general solution, if possible. Otherwise find a relation that defines the solutions implicitly: xy' - y=x(1 + e^(-y/x))

calculus 3 and 4

Show all work, don't explain each step. Please DON'T submit answers back to me as an attachment. Thank you. First determine if the equation is exact. If it is exact, find the general solution, or at least a relation that defines the solutions implicitly: [cos(x^2 + y) - 3xy^2]y' + 2x cos(x^2 + y) - y^3=0

calculus 3 and 4

Show all work, don't explain each step. Please DON'T submit answers back to me as an attachment. Thank you. Using: d tan^-1 (x/y)=(y dx - x dy)/(x^2 + y^2), and ½ d ln(x^2 + y^2)=(x dx + y dy)/(x^2 + y^2) find integrating factors for, and solve, the following equation: (2x^(2)y + 2y^3 - x) (dy ...continues