Identify the number of moles of each element present in one mole of NH NO3.

Find the general solution of the given higher-order differential equation. d3u dt3 + d2u dt2 − 2u = 0

STALIN [3.7K]

$\dfrac{\mathrm d^3u}{\mathrm dt^3}+\dfrac{\mathrm d^2u}{\mathrm dt^2}-2u=0$

This ODE has characteristic equation

$r^3+r^2-2=(r^3-r)+(r^2+r-2)=r(r^2-1)+(r+2)(r-1)$

$=(r(r+1)+(r+2))(r-1)=(r^2+2r+2)(r-1)=0$

which has roots at $r=1,-1\pm i$ . Then the characteristic solution to the ODE is

$u(t)=C_1e^t+C_2e^{(-1+i)t}+C_3e^{(-1-i)t}$

$\implies\boxed{u(t)=C_1e^t+C_2e^{-t}\cos t+C_3e^{-t}\sin t}$

6 0

3 years ago

What is 1234 ÷ 60?<br><img src="https://tex.z-dn.net/?f=1234%20%5Cdiv%2060" id="TexFormula1" title="1234 \div 60" alt="1234 \div

sineoko [7]

<h2>As a decimal: 20.56667</h2><h2>As fractions: $\frac{617}{30}$ OR $20\frac{17}{30}$ </h2>

3 0

3 years ago

How many variable terms are in the expression 3x3y + 5x2 − 4y + z + 9? (Input a numeric value only.)

Anarel [89]

Answer:

4

Step-by-step explanation:

A variable term is a mathematical term in which a variable is by itself or is connected to a coefficient(s).

3x3y, 5x2, −4y, z.

7 0

2 years ago

On the graph shown, what is f(-1)? (5 points) The first segment joints the point negative three comma five exclusively and negat

tatiyna

ANSWER

$f( - 1) = 2$

EXPLANATION

The given function is a piecewise defined function.

$f( - 1)$
is the y-value that corresponds to
$x = - 1.$

To determine that y-value, we need to trace from
$x = - 1$
to where it meets the graph.

We then trace to the y-axis to determine the corresponding y-value as shown in the diagram.

From the graph, we can see that this x-value corresponds to a y-value of
$2$

This implies that, when
$x = - 1,y = 2$

Therefore
$f( - 1) = 2$
See graph.