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Ede4ka [16]
2 years ago
14

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

Mathematics
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

  1. 130
  2. 50
  3. 50
  4. 130
  5. 130
  6. 50
  7. 50
  8. 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
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