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3 years ago

14

Which is the graph of f(x) =2(3)x?

1 answer:

inn [45]3 years ago

5 0

Two of the points are (0,0) and (1,6)

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D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x

MA_775_DIABLO [31]

The solution depends on the value of $k$ . To make things simple, assume $k>0$ . The homogeneous part of the equation is

$\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0$

and has characteristic equation

$r^2-16k=0\implies r=\pm4\sqrt k$

which admits the characteristic solution $y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}$ .

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be $y_p=ae^{4x}+be^x$ . Then

$\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x$

So you have

$16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x$
$(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x$

This means

$16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}$
$b(1-16k)=30\implies b=\dfrac{30}{1-16k}$

and so the general solution would be

$y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x$

8 0

2 years ago

Im running out of time Somebody help me out please

kobusy [5.1K]

Answer:

3, 4, and 5

Step-by-step explanation:

To put it simply, 3 + 4 + 5 = 12 and the numbers are consecutive, next to each other.

The method:

The three consecutive numbers could be called x, x + 1, and x + 2 and we know that x + x + 1 + x + 2 = 12

This can be simplified to 3x + 3 = 12. Next, subtract 3 from both sides to get 3x = 9. Now, divide both sides by 3 to get x = 3.

This means that the first number is 3 and the other numbers are 4 (3 + 1) and 5 (3 + 2).

Hope this helps!

8 0

2 years ago

Read 2 more answers

Nate paid $108 for a food bill that included a 15% tip. Using a decimal equivalent to the percent, write an equation to find the

spin [16.1K]

The solution is in the attachment

3 0

3 years ago

HELP PLEASE!!!!! WILL MARK AS BRAINLIEST!!!!

expeople1 [14]

ASA we need a second angle that is next to the side

SAS we need a side next to the angle

Choice B

5 0

3 years ago

I REALLY NEED HELP PLEASE 30 POINTS AND BRIANLIEST

Mademuasel [1]

Answer:

C is the closest one but it should be -472 instead -475

Step-by-step explanation:

just insert X in the formulas and compare to P

7 0

3 years ago