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3 years ago

12

Find any values of the variable for which each rational expression is undefined. Write answers with the symbol ≠.

1 answer:

astra-53 [7]3 years ago

4 0

Answer:

x $\neq$ 3

Step-by-step explanation:

if x = 3 then the rational expression 4 / (x - 3) is undefined

because we get 4/0 = undefined .

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What is the equation of (0,2) and (3,0)

ivolga24 [154]

Let's first find the slope. This is (y_2 - y_1)/(x_2 - x_1), where (x_1, y_1) and (x_2, y_2) are points.

For this problem, our slope is (0 - 2)/(3 - 0) = -2/3.

We can now use the point-slope formula to find the equation of our line:
(y - y_1) = m(x - x_1)
(y - 2) = -2/3(x - 0)
y - 2 = (-2/3)x
y = (-2/3)x + 2

The equation of our line is $\boxed{y = -\frac{2}{3}x + 2}$ .

8 0

3 years ago

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

<img src="https://tex.z-dn.net/?f=%5Csqrt25" id="TexFormula1" title="\sqrt25" alt="\sqrt25" align="absmiddle" class="latex-formu

anzhelika [568]

Answer:

Rational

Step-by-step explanation:

The square root of 25 is 5, which is a rational number.

4 0

3 years ago

Read 2 more answers

I need help with all three please help!

denis-greek [22]

Answer:

c

a

b

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

True or False: A decimeter, a centimeter and a millimeter are all smaller than a meter.

aev [14]

<h2>Answer:</h2><h2>True. A decimeter, a centimeter and a millimeter are all smaller than a meter.</h2>

Step-by-step explanation:

Convert all the units to metres for compariosn.

By metric conversion,

1 decimetre = 0.1 metre

1 centimetre = 0.01 metre

1 millimetre = 0.001 metre

Based on the above conversions, a decimeter, a centimeter and a millimeter are all smaller than a meter. Therefore the given statement is true.

3 0

3 years ago