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3 years ago

Select the correct answer from each drop-down menu.

Mathematics

1 answer:

Elodia [21]3 years ago

8 0

Answer:

The left end approaches to + Infinite being an exponential function, and the right end to 0

Step-by-step explanation:

we have to remember the exponential function, the best way to find the answer is plotting the graph or arranging a table of values.

As you can see in the attached graph the y axis gets closer and closer to 0 as it moves forward in the x axis, and as it moves to the left the y axis starts increasing rapidly.

Also you got to keep in mind the way that functions behave in terms of the sign of its variable. for example the 10 in this equation only makes the curve to get wider, but if you change the sign to minus, the answer would be different.

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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

2 years ago

-3(n + 5) = 12 solve^

UNO [17]

Answer:

n= 1

Step-by-step explanation:

-3n + 15 =12

-15. -15

-3n= - 3

÷-3 ÷-3

n= 1

5 0

3 years ago

Read 2 more answers

Mark thinks the equation y=6x+4 will match the red solid graph. Mia thinks it will match the blue dotted graph. Who’s right? Exp

Rudiy27

Answer:

Technically neither, but Mia is correct.

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Since our slope m is equal to 6, it is a positive number. That means that the slope/line will be positive, so the line should be going up, not down. That means the blue line would be correct. Therefore, Mia is correct.

Technicality:

Since the blue line is dotted, the equation should be a inequality and not a linear equation. No solutions on the line would technically work. If the equation was y < 6x + 4 or something with an inequality sign, then it would be correct.

6 0

3 years ago

I need help with this question and it’s very urgent!!!!

andreev551 [17]

Answer:

AAS

Step-by-step explanation:

8 0

3 years ago

Please help compare these integers by typing the symbol that would make the statement true

faust18 [17]

>
Positive integers are always greater.

3 0

3 years ago