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4 years ago

What kinds of asymptotes are possible for a rational function?

Mathematics

1 answer:

exis [7]4 years ago

7 0

Vertical or horizontal; it depends on what the function is.

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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

4 years ago

Please Help Me :((.

Sidana [21]

Answer:

4.2 h

Step-by-step explanation:

12 * (50%-15%) = 4.2 h

8 0

3 years ago

Perimeter of a rectangle is 96m. if it's length is 3 times it's width , then find it's length and breadth.

Stolb23 [73]

Answer:

breadth = 12

length = 36

Step-by-step explanation:

let the breadth be 'x'

length = 3x

p = 2l + 2b

96 = 2(3x) + 2(x)

x = 12

7 0

4 years ago

A bulb can either be on or off. A board contains 20 bulbs connected to a randomization circuit that lights up a random sequence

Step2247 [10]

The chance that any given bulb is on is equal to 1/2. The chance that all twenty bulbs are on at the same time is $(\frac{1}{2}) ^{20} = \frac{1^{20}}{2^{20}} = \frac{1}{1048576}$

8 0

3 years ago

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What is the slope of the line?

avanturin [10]

3/4 To find the slope of a line you need to do rise/run. you find two solid points meaning find two points are exactly on a intersection. Then you count up how much it needs to the point then count across to the next point

8 0

3 years ago

Read 2 more answers