I need help on this fast pls help me

Solve the system using any method. Show your work. { 3 x + y = 4 − 3 x − y = − 8

prisoha [69]

Answer:

No solution

Step-by-step explanation:

3 x + y = 4 (1)

− 3 x − y = − 8 (2)

Add (1) and (2)

0 + 0 = -4

0 = -4 is a false statement

So, no solution

5 0

3 years ago

Use undetermined coefficient to determine the solution of:y"-3y'+2y=2x+ex+2xex+4e3x

Kitty [74]

First check the characteristic solution: the characteristic equation for this DE is

r ² - 3r + 2 = (r - 2) (r - 1) = 0

with roots r = 2 and r = 1, so the characteristic solution is

y (char.) = C₁ exp(2x) + C₂ exp(x)

For the ansatz particular solution, we might first try

y (part.) = (ax + b) + (cx + d) exp(x) + e exp(3x)

where ax + b corresponds to the 2x term on the right side, (cx + d) exp(x) corresponds to (1 + 2x) exp(x), and e exp(3x) corresponds to 4 exp(3x).

However, exp(x) is already accounted for in the characteristic solution, we multiply the second group by x :

y (part.) = (ax + b) + (cx ² + dx) exp(x) + e exp(3x)

Now take the derivatives of y (part.), substitute them into the DE, and solve for the coefficients.

y' (part.) = a + (2cx + d) exp(x) + (cx ² + dx) exp(x) + 3e exp(3x)

… = a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)

y'' (part.) = (2cx + 2c + d) exp(x) + (cx ² + (2c + d)x + d) exp(x) + 9e exp(3x)

… = (cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)

Substituting every relevant expression and simplifying reduces the equation to

(cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)

… - 3 [a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)]

… +2 [(ax + b) + (cx ² + dx) exp(x) + e exp(3x)]

= 2x + (1 + 2x) exp(x) + 4 exp(3x)

… … …

2ax - 3a + 2b + (-2cx + 2c - d) exp(x) + 2e exp(3x)

= 2x + (1 + 2x) exp(x) + 4 exp(3x)

Then, equating coefficients of corresponding terms on both sides, we have the system of equations,

x : 2a = 2

1 : -3a + 2b = 0

exp(x) : 2c - d = 1

x exp(x) : -2c = 2

exp(3x) : 2e = 4

Solving the system gives

a = 1, b = 3/2, c = -1, d = -3, e = 2

Then the general solution to the DE is

y(x) = C₁ exp(2x) + C₂ exp(x) + x + 3/2 - (x ² + 3x) exp(x) + 2 exp(3x)

4 0

3 years ago

Two sides of a triangle are given as 28 inches and 42 inches. find all possible lengths for the third side of the triangle

timofeeve [1]

The longest side of a triangle must be less than the sum of the other 2 sides

2 senarios

the 3rd side is the longest
the 3rd side is not the longest

for the 3rd side is the longest

3rdside<28+42
3rdside<70

for 3rd side isn't the longest
42 is longest
42<28+3rdside
14<3rdside

so we've got
3rdside<70 and 14<3rdside

so
14<3rdside<70

the 3rd side can be any number from 14in to 70in except 14in and 70in

6 0

3 years ago

What is the value of x? Enter your answer in the box. X =

melamori03 [73]

Answer:

x=54

Step-by-step explanation:

2x + 2 = 3x - 52

subtract 2x from both sides, now u have:

2 = x - 52

add 52 from both sides, now u have

54 = x

7 0

3 years ago

Which of the following best describes the solution to the system of equations below? -6x + y = -3 7x - y = 3

rusak2 [61]

Answer:

y= -3

x= 0

Step-by-step explanation:

I will give the explanation in picture, hope you can understand it.

7 0

3 years ago

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