Homework Answers
The given equations are each a equations of hyperbola. For solving a equation in 2 variable we need minimum 2 equations. So no unique solution can exist in each case. If 2 equations are given in a system then we will get two geometric figures and their points of intersection will give solution in ordered pair (x,y). So we will not get any unique solution in question (a), (b) and (c).
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34.2. For each of the following equations, either find a solution (x, y) in positive integers or explain why no such so...
Find all integers x, y, 0 < x, y < n, that satisfy each of the...
Find all integers x, y, 0 < x, y < n, that satisfy each of the following pairs of congruences. If no solutions exist, explain why. (a) x + 5y = 3(mod n), and 4x + y = 1(mod n), for n = 8. (b) 7x + 2y = 3(mod n), and 9x + 4y = 6(mod n), for n=5.
explain why there are no integers x and y such that 25x+30y=1
explain why there are no integers x and y such that 25x+30y=1
34.1. In this chapter we have shown that Pell's equation x2- Dy2-1 always has a so- lution in positive integers. Th...
34.1. In this chapter we have shown that Pell's equation x2- Dy2-1 always has a so- lution in positive integers. This exercise explores what happens if the 1 on the right-hand side is replaced by some other number (a) For each 2 < D < 15 that is not a perfect square, determine whether or not the equation x2 - Dy2 - -1 has a solution in positive integers. Can you determinea pattern that lets you predict for which D's...
for differential equations 1. Identify each of the following differential equations as either Separable, Homogeneous, Linear...
for
differential equations
1. Identify each of the following differential equations as either Separable, Homogeneous, Linear Bernoulli, or Exact and solve the equation using the method of the type you have identified. Many can be classified in multiple ways, it is not necessary to list all possibilities. (3xy2 +2ycos x)+y'-y sin x-x =0 Туре: A. dx General Solution: B. (4xy+xy)2x+ xy2 dx Туре: General Solution: Туре: C. y'y'y+1 General Solution: (3x'y+e')-(2y-x-xe)dy Туре: D. dx General Solution: Туре: dy E. =y(xy-1)...
Find the solution to the system of differential equations: x' y' = = y - x...
Find the solution to the system of differential equations: x' y' = = y - x +t, y, 2(0) = 3 y(0) = 4 (t) = er help (formulas) help (formulas) y(t) =
For each of the following, find the pdf of Y (e) Y =In X and (п+...
For each of the following, find the pdf of Y (e) Y =In X and (п+ m+1)! -"(1 - x)" fx (x) = n!m! <1 and m and n are positive integers where 0 (f) Y e and 1 fx(x) e)2/2 where 0 < oo and o2 is a positive constant (i) Y 1 X2 and fx (x)=3(x 1)2, -1 < x <1
Q7) Find the general solution for each of the following equations a) y" +44't5y=o b) учу...
Q7) Find the general solution for each of the following equations a) y" +44't5y=o b) учу – 2 = + Чg + цо y"
evaluate each limit or explain why it does not exist (b) 4x² - y² lim (x,y)+(0,0)...
evaluate each limit or explain why it does not exist
(b) 4x² - y² lim (x,y)+(0,0) x2 + 2y2
Solve the following system of equations. X+ y+ z- w = 4 3x + y- z+...
Solve the following system of equations. X+ y+ z- w = 4 3x + y- z+ w = 10 x- 4y + 32+ w = -5 -x- y+ 2+ 4w = 4 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. There is one solution. The solution is ). (Type integers or simplified fractions.) O B. There are infinitely many solutions. The solutions are ( (Type integers or simplified fractions.)...
1. (each 5pts) Find the solution of the following differential equations. (a) y" + 6y' +9y=0...
1. (each 5pts) Find the solution of the following differential equations. (a) y" + 6y' +9y=0 which satisfies yo)= 4 and V = 4 (b) v- 5y' +6y=0 which satisfies y(o)=1 and y (0)=2
Find all integers x, y, 0 < x, y < n, that satisfy each of the following pairs of congruences. If no solutions exist, explain why. (a) x + 5y = 3(mod n), and 4x + y = 1(mod n), for n = 8. (b) 7x + 2y = 3(mod n), and 9x + 4y = 6(mod n), for n=5.
34.1. In this chapter we have shown that Pell's equation x2- Dy2-1 always has a so- lution in positive integers. This exercise explores what happens if the 1 on the right-hand side is replaced by some other number (a) For each 2 < D < 15 that is not a perfect square, determine whether or not the equation x2 - Dy2 - -1 has a solution in positive integers. Can you determinea pattern that lets you predict for which D's...
for
differential equations
1. Identify each of the following differential equations as either Separable, Homogeneous, Linear Bernoulli, or Exact and solve the equation using the method of the type you have identified. Many can be classified in multiple ways, it is not necessary to list all possibilities. (3xy2 +2ycos x)+y'-y sin x-x =0 Туре: A. dx General Solution: B. (4xy+xy)2x+ xy2 dx Туре: General Solution: Туре: C. y'y'y+1 General Solution: (3x'y+e')-(2y-x-xe)dy Туре: D. dx General Solution: Туре: dy E. =y(xy-1)...
Find the solution to the system of differential equations: x' y' = = y - x +t, y, 2(0) = 3 y(0) = 4 (t) = er help (formulas) help (formulas) y(t) =
For each of the following, find the pdf of Y (e) Y =In X and (п+ m+1)! -"(1 - x)" fx (x) = n!m! <1 and m and n are positive integers where 0 (f) Y e and 1 fx(x) e)2/2 where 0 < oo and o2 is a positive constant (i) Y 1 X2 and fx (x)=3(x 1)2, -1 < x <1
Q7) Find the general solution for each of the following equations a) y" +44't5y=o b) учу – 2 = + Чg + цо y"
evaluate each limit or explain why it does not exist
(b) 4x² - y² lim (x,y)+(0,0) x2 + 2y2
Solve the following system of equations. X+ y+ z- w = 4 3x + y- z+ w = 10 x- 4y + 32+ w = -5 -x- y+ 2+ 4w = 4 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. There is one solution. The solution is ). (Type integers or simplified fractions.) O B. There are infinitely many solutions. The solutions are ( (Type integers or simplified fractions.)...
1. (each 5pts) Find the solution of the following differential equations. (a) y" + 6y' +9y=0 which satisfies yo)= 4 and V = 4 (b) v- 5y' +6y=0 which satisfies y(o)=1 and y (0)=2
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