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3 years ago

Is y = x + 6 and y = x + 4 parallel, perpendicular or neither

Mathematics

1 answer:

djverab [1.8K]3 years ago

5 0

Answer:

Parallel

Step-by-step explanation:

y=x+6

y=x+4

--------

y=mx+b where m=slope.

-------------

These 2 lines have same slopes, which means/indicates parallel lines.

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Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x

djverab [1.8K]

I'll assume the ODE is

$y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}$

Solve the homogeneous ODE,

$y'' - 3y' + 2y = 0$

The characteristic equation

$r^2 - 3r + 2 = (r - 1) (r - 2) = 0$

has roots at $r=1$ and $r=2$ . Then the characteristic solution is

$y = C_1 e^x + C_2 e^{2x}$

For nonhomogeneous ODE (1),

$y'' - 3y' + 2y = e^x$

consider the ansatz particular solution

$y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x$

Substituting this into (1) gives

$a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1$

For the nonhomogeneous ODE (2),

$y'' - 3y' + 2y = e^{2x}$

take the ansatz

$y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}$

Substitute (2) into the ODE to get

$b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1$

Lastly, for the nonhomogeneous ODE (3)

$y'' - 3y' + 2y = e^{-x}$

take the ansatz

$y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}$

and solve for $c$ .

$ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16$

Then the general solution to the ODE is

$\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}$

6 0

1 year ago

What is the are of the sqare? (P=4s) (A=s2) the bottom of the sqare has a perimeter of 3ft

Anettt [7]

Answer:

You plug in 3 as s. So ur formula is P=4(3)

P=12 ft

Step-by-step explanation:

yes im answering this from a year later i just need like 3 points sry

6 0

2 years ago

You need 8 oz of red paint and 12 oz of blue paint to make purple paint. How much red paint is needed for 15 oz of blue paint?

olga2289 [7]

Answer:

10oz

Step-by-step explanation:

Solve

4 0

2 years ago

Plzz i need help with this can somebody help me?

Olin [163]

Answer:

the answer is b

Step-by-step explanation:

if u divide .14 by .2

its gonna give u .8

2 times 8 is 16 but there are two decimals so its .16

hope this helps

6 0

2 years ago

Based on the information in the table what is the probability of being a girl and choosing lemonade?

tresset_1 [31]

Using it's concept, it is found that the probability of being a girl and choosing lemonade is given by:

b. 0.2.

<h3>What is a probability?</h3>

A probability is given by the <u>number of desired outcomes divided by the number of total outcomes</u>.

In this problem, out of 130 people, 26 are girls who choose lemonade, hence the probability is given by:

p = 26/130 = 0.2, which means that option b is correct.

More can be learned about probabilities at brainly.com/question/14398287

#SPJ1

5 0

2 years ago