. Which Statement Is True??

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

3 years ago

A typical cup of coffee contains about 100 mg of caffeine and every hour approximately 16% ofthe amount of caffeine inthe body i

Over [174]

Answer:

a) $\frac{dC}{dt} = rC$

And for this case we can rewrite the model like this:

$\frac{dC}{C} = r dt$

If we integrate both sides we got:

$ln C = rt + k$

If we use exponentials for both sides we got:

$C = e^{rt} e^k = C_o e^{rt}$

For this case $C_o = 100 mg$ and r = -0.16

So then our model would be given by:

$C(t) = 100 e^{-0.16 t}$

Where t represent the number of hours

b) $C(5) = 100 e^{-0.16*5}= 44.9329$

Step-by-step explanation:

Part a

For this case we can assume the proportional model given by:

$\frac{dC}{dt} = rC$

And for this case we can rewrite the model like this:

$\frac{dC}{C} = r dt$

If we integrate both sides we got:

$ln C = rt + k$

If we use exponentials for both sides we got:

$C = e^{rt} e^k = C_o e^{rt}$

For this case $C_o = 100 mg$ and r = -0.16

So then our model would be given by:

$C(t) = 100 e^{-0.16 t}$

Where t represent the number of hours

Part b

For this case we can replace the value t=5 into the model and we got:

$C(5) = 100 e^{-0.16*5}= 44.9329$

7 0

3 years ago

Solve ASAP<br>i dont get it

andreev551 [17]

The slope is the coefficient of x when the coefficient of y is 1.
The slope is -0.5
The y-intercept is where x=0
y = 17 - 0.5 (0)
y = 17
The y-intercept is 17.

5 0

4 years ago

What is the value of r in the equation -3(4r - 8)=-36

Marianna [84]

Answer:

r=5

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

-3*(4*r-8)-(-36)=0

Step by step solution :

Step 1 :

Step 2 :

Pulling out like terms :

2.1 Pull out like factors :

4r - 8 = 4 • (r - 2)

Equation at the end of step 2 :

(0 - 12 • (r - 2)) - -36 = 0

Step 3 :

Step 4 :

Pulling out like terms :

4.1 Pull out like factors :

60 - 12r = -12 • (r - 5)

Equation at the end of step 4 :

-12 • (r - 5) = 0

Step 5 :

Equations which are never true :

5.1 Solve : -12 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

5.2 Solve : r-5 = 0

Add 5 to both sides of the equation :

r = 5

One solution was found :

r = 5

brainliest pllzz thx god bless

3 0

3 years ago

Read 2 more answers

How can I find the x-intercept in a graph if the equation is 2x+3y=6

Varvara68 [4.7K]

Answer:

Step-by-step explanation:

First you would need to multiply 3y by zero since when finding x intercept, Y is always zero.

2x=6

next you would divide both sides by 2 and you get

X= 3 The ordered pair would be (3,0)

8 0

4 years ago