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2 years ago

14

Which of the following equations is equivalent to y = lnx?

1 answer:

harkovskaia [24]2 years ago

4 0

Step-by-step explanation:

e^ln x - ln xy is equal to (a) y (b) 1/y (c) x (d) 1/x (e) none of these Which of the following equations is equivalent to the equation y = 5^x? (a) y = ln(5x) (b) y = e^5 ln x (c) y = e^x ln 5 (d) y = x ln 5 (e) none of these When $400 is invested in an account that earns 7.5% annualinterest, compounded quarterly, the accumulated value after 5 years (to the nearest cent) is (a) $581.99 (b) $579.98 (c) $574.25 (d) $550.00 (e) none of these

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Consider the system of differential equations dxdt=−4ydydt=−4x. Convert this system to a second order differential equation in y

koban [17]

$\dfrac{\mathrm dy}{\mathrm dt}=-4x\implies x=-\dfrac14\dfrac{\mathrm dy}{\mathrm dt}\implies\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}$

Substituting this into the other ODE gives

$-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}=-4y\implies y''-16y=0$

Since $x(t)=-\dfrac14y'(t)$ , it follows that $x(0)=-\dfrac14y'(0)=4\implies y'(0)=-16$ . The ODE in $y$ has characteristic equation

$r^2-16=0$

with roots $r=\pm4$ , admitting the characteristic solution

$y_c=C_1e^{4t}+C_2e^{-4t}$

From the initial conditions we get

$y(0)=5\implies 5=C_1+C_2$

$y'(0)=16\implies-16=4C_1-4C_2$

$\implies C_1=\dfrac12,C_2=\dfrac92$

So we have

$\boxed{y(t)=\dfrac12e^{4t}+\dfrac92e^{-4t}}$

Take the derivative and multiply it by -1/4 to get the solution for $x(t)$ :

$-\dfrac14y'(t)=\boxed{x(t)=-\dfrac12e^{4t}+\dfrac92e^{-4t}}$

7 0

3 years ago

2.86 = ? tenths + 6 hundredths =

kherson [118]

To get 2.8 from 0.1 you have to multiply by 28. So 28 tenths. Which leaves 0.06 which is 0.01 times 6. So 6 hundredths

5 0

3 years ago

Read 2 more answers

Answer this quick I have 20 minutes<br> 25 points

e-lub [12.9K]

The answer is A. You can comment if u want an explanation :)

6 0

2 years ago

What id the greatest common factor shared by 24 and 54

Marysya12 [62]

Answer:

6.

Step-by-step explanation:

3 0

2 years ago

Plz help fifty points

likoan [24]

Answer:

for question 13

130
50
50
130
130
50
50
130

Step-by-step explanation:

for 14

x. 150

y. 15

z. 150

i cant say that this is totally correct but im taking a educated guess

7 0

2 years ago

Read 2 more answers