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3 years ago

A system is linear if it has

Engineering

1 answer:

Nadusha1986 [10]3 years ago

6 0

A system is a linear system if all equations inside the system can be simplified into the form,

$y=mx+n$

aka linear form of a linear equation.

So to sum up, a system is linear if all equations are linear equations.

Hope this helps :)

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A force is specified by the vector F= 160i + 80j + 120k N. Calculate the angles made by F with the positive x-, y-, and z-axis.

Rashid [163]

Answer:

1) Angle with x-axis = 42.03 degrees

2) Angle with y-axis =68.2 degrees

3) Angle with z-axis = 56.14 degrees

Explanation:

given any vector $\overrightarrow{r}=x\widehat{i}+y\widehat{j}+z\widehat{k}$

and any x axis the angle between them is given by

$\theta_x =cos^{-1}(\frac{\overrightarrow{r}\cdot\widehat{i}}{\sqrt{x^2+y^2+z^2}} )\\\\\theta_x=cos^{-1}(\frac{x\cdot i}{\sqrt{x^2+y^2+z^2}} )$

Applying values we get

$\theta_x=cos^{-1}(\frac{160}{\sqrt{160^2+80^2+120^2}} )=42.03^{o}$

Angle between the vector and y axis is given by

$\theta_y =cos^{-1}(\frac{\overrightarrow{r}\cdot\widehat{j}}{\sqrt{x^2+y^2+z^2}} )\\\\\theta_y=cos^{-1}(\frac{y\cdot j}{\sqrt{x^2+y^2+z^2}} )$

Applying values we get

$\theta_x=cos^{-1}(\frac{80}{\sqrt{160^2+80^2+120^2}} )=68.2^{o}$

Similarly angle between z axis and the vector is given by

$\theta_z =cos^{-1}(\frac{\overrightarrow{r}\cdot\widehat{k}}{\sqrt{x^2+y^2+z^2}} )\\\\\theta_x=cos^{-1}(\frac{z\cdot k}{\sqrt{x^2+y^2+z^2}} )$

Applying values we get

$\theta_z=cos^{-1}(\frac{120}{\sqrt{160^2+80^2+120^2}} )=56.145^{o}$

5 0

4 years ago

What is often the first step in the formation of a volcano?

Rasek [7]

Answer:

mantle rocks begin to melt

Explanation:

melt when temperature raises, pressure lowers or water is added

3 0

3 years ago

The displacement volume of an internal combustion engine is 2.2 liters. The processes within each cylinder of the engine are mod

soldier1979 [14.2K]

Answer:

A) 14.75

B) 3.36Kj

C) 2384.2k

D) 117.6kW

E) 57.69%

Explanation:

Attached is the full solutions.

5 0

4 years ago

The motion of a particle is defined by the relation x = t3 – 6t2 + 9t + 3, where x and t are expressed in feet and seconds, resp

Semmy [17]

Answer:

a. t=3secs and t=1sec

position is -7ft,acceleration is 18fts⁻², total distance travelled is 120ft

Explanation:

the displacement is define as

x=t³-6t²+9t+3·

since we are giving the position as a function of time, the velocity is the derivative of the position,

v=dx/dt

v=d(t³-6t²+9t+3)/dt

recall for y=axⁿ the derivative

dy/dx=a*nxⁿ⁻¹ and the derivative of a constant is zero

hence

V=3t²-12t+9

for V=0,

equivalent to t²-4t+3

solving the quadratic equation, we arrive at

(t-3)(t-1)=0

either t=3 or t=1

hence,at 3secs and 1sec the velocity is zero.

To determine the position at t=5, we substitute t=5 into

t³-6t²+9t+3

(5)³-6(5)²+9(5)+3

125-180+45+3

-7ft

The position at t=5 is -7ft

To determine the acceleration, we differentiate the velocity

a=dv/dt

a=d(3t²-12t+9)/dt

a=6t-12

at t=5

a=6(5)-12

a=18fts⁻²

Next we determine the distance covered at t=5

velocity =total distance travelled/total time taken

velocity=3t²-12t+9

V=3(25)-12(5)+9

V=24ft/s

Hence total distance travelled in t=5 is

24*5=120ft

6 0

3 years ago

An insulated rigid tank is divided into two compartments of different volumes. Initially, each compartment contains the same ide

storchak [24]

Answer:

Explanation:

Given that

Mass of 1 = $m_1$

Mass of 2 = $m_2$

Temperature in 1 = $T_1$

Temperature in 2 = $T_2$

Pressure remains i the group apartment

The closed system and energy balance is

$E_{in}-E_{out}=\Delta E_{system}$

The kinetic energy and potential energy are negligible

since it is insulated tank ,there wont be eat transfer from the system

And there is no work involved

$\Delta U = 0$

Let the final temperature be final temperature

$m_1+c_v(T_3-T_1)+m_2c_v(T_3+T_2)=0\\\\m_1+c_v(T_3-T_1)=m_2c_v(T_2-T_3)---(i)$

Using mass balance

$m_3+m_2+m_1$

from eqn i

$m_1+c_v(T_3-T_1)=m_2c_v(T_2-T_3)m_1T_3-m_1T_1=m_2T_2-m_2T_3\\\\m_1T_3+m_2T_3=m_2T_2+m_1T_1\\\\(m_1+m_2)T_3=m_1T_1+m_2T_2\\\\(m_1)T_3=m_1T_1+m_2T_2\\\\T_3=\frac{m_1T_1_m_2T_2}{m_3}$

Therefore the final temperature can be express as

$\large \boxed {T_3=\frac{m_1}{m_3} T_1+\frac{m_2}{m_3}T_2 }$

8 0

3 years ago

A system is linear if it has​

A system is linear if it has