A piston-cylinder device initially at 0.45-m3 contains nitrogen gas at 600 kPa and 300 K. Now the gas is compressed isothermally to a volume of 0.2 m3. The work done on the gas during this compression process is _____ kJ.

Answer:

height ≈ 60.60 m

Explanation:

The surveyor is trying to find the height of the hill . He takes a sight on the top of the hill and finds the angle of elevation is 40°. The distance from the hill where he measured the angle of elevation of 40° is not known.

Now he moves 150 m on level ground directly away from the hill and take a second sight from this point and measures the angle of elevation as 22°. This illustration forms a right angle triangle. The opposite side of the triangle is the height of the hill. The adjacent side of the triangle which is 150 m is the distance on level ground directly away from the hill.

Using tangential ratio,

tan 22° = opposite/adjacent

tan 22° = h/150

h = 150 × tan 22°

h = 150 × 0.40402622583

h = 60.6039338753

height ≈ 60.60 m

Answer:

The function is [tex]-\sin x[/tex] and the constant of integration is [tex]C = - 1[/tex].

Explanation:

The resultant expression is equal to the sum of a constant multiplied by the integral of a given function and an integration constant. That is:

[tex]a = k\cdot \int\limits {f(x)} \, dx + C[/tex]

Where:

[tex]k[/tex] - Constant, dimensionless.

[tex]C[/tex] - Integration constant, dimensionless.

By comparing terms, [tex]k = 2[/tex], [tex]C = -1[/tex] and [tex]\int {f(x)} \, dx = \cos x[/tex]. Then, [tex]f(x)[/tex] is determined by deriving the cosine function:

[tex]f(x) = \frac{d}{dx} (\cos x)[/tex]

[tex]f(x) = -\sin x[/tex]

The function is [tex]-\sin x[/tex] and the constant of integration is [tex]C = - 1[/tex].

Answer:

In consolidated AB Co 300 shares.

Explanation:

Consolidation is a process in which two different organizations are united. In this question A Co and B Co are consolidated and a new Co names AB Co is formed. The shares of both the companies will be combined and their total share capital will be increased.

Answer:

See explanation

Explanation:

Solution:-

- Three students measure the volume of a liquid sample which is 6.321 L.

- Each student measured the liquid sample 4 times. The data is provided for each measurement taken by each student as follows:

                                                 Students

                      Trial          A            B               C

                         1            6.35        6.31          6.38

                        2            6.32        6.31          6.32

                        3            6.33        6.32         6.36

                        4            6.36        6.35         6.36

- We will define the two terms stated in the question " precision " and "accuracy"

- Precision refers to how close the values are to the sample mean. The dense cluster of data is termed to be more precise. We will use the knowledge of statistics and determine the sample standard deviation for each student.

- The mean measurement taken by each student would be as follows:

                       [tex]E ( A ) = \frac{6.35 +6.32+6.33+6.36}{4} \\\\E ( A ) = 6.34\\\\E ( B ) = \frac{6.31 +6.31+6.32+6.35}{4} \\\\E ( B ) = 6.3225\\\\E ( C ) = \frac{6.38 +6.32+6.36+6.36}{4} \\\\E ( C ) = 6.355\\[/tex]

- The precision can be quantize in terms of variance or standard deviation of data. Therefore, we will calculate the variance of each data:

                        [tex]Var ( A ) = \frac{6.35^2+6.32^2+6.33^2+6.36^2}{4} - 6.34^2\\\\Var ( A ) = 0.00025\\\\Var ( B ) = \frac{6.31^2+6.31^2+6.32^2+6.35^2}{4} - 6.3225^2\\\\Var ( B ) = 0.00026875\\\\Var ( C ) = \frac{6.38^2+6.32^2+6.36^2+6.36^2}{4} - 6.355^2\\\\Var ( C ) = 0.000475\\[/tex]

- We will rank each student sample data in term sof precision by using the values of variance. The smallest spread or variance corresponds to highest precision. So we have:

                   Var ( A )          <          Var ( B )        <    Var ( C )

                   most precise                                      Least precise

- Accuracy refers to how close the sample mean is to the actual data value. Where the actual volume of the liquid specimen was given to be 6.321 L. We will evaluate the percentage difference of sample values obtained by each student .

                       [tex]P ( A ) = \frac{6.34-6.321}{6.321}*100= 0.30058\\\\P ( B ) = \frac{6.3225-6.321}{6.321}*100= 0.02373\\\\P ( C ) = \frac{6.355-6.321}{6.321}*100= 0.53788\\[/tex]

- Now we will rank the sample means values obtained by each student relative to the actual value of the volume of liquid specimen with the help of percentage difference calculated above. The least percentage difference corresponds to the highest accuracy as follows:

                   P ( B )         <       P ( A )         <      P ( C )

            most accurate                                least accurate

Mathematical modeling aids in technological design by simulating how proposed system might behave. The correct option is 2.

Mathematical modelling describes a real world problem in mathematical terms or in the form of equations. This makes an engineer to discover new features about the problem and designer to alter his design for better function and output.

Mathematical models allow engineers and designers to understand how the proposed model and actual prototype will be produced.

Thus, the correct option is 2.

Learn more about mathematical modelling

https://brainly.com/question/731147

#SPJ2

Answer:

Explanation:

The value of a will be zero as it is provided that the particle is on the x-axis.

Calculate the velocity of particles along x-axis.

[tex]{\bf{V}} = 2{x^2}t{\bf{\hat i}} + [4y(t - 1) + 2{x^2}t]{\bf{\hat j}}{\rm{ m/s}}[/tex]

Substitute 0 for y.

[tex]\begin{array}{c}\\{\bf{V}} = 2{x^2}t{\bf{\hat i}} + \left( {4\left( 0 \right)\left( {t - 1} \right) + 2{x^2}t} \right){\bf{\hat j}}{\rm{ m/s}}\\\\ = 2{x^2}t{\bf{\hat i}} + 2{x^2}t{\bf{\hat j}}{\rm{ m/s}}\\\end{array}[/tex]

Here,

[tex]A = 2{x^2}t \ \ and\ \ B = 2{x^2}t[/tex]

Calculate the magnitude of vector V .

[tex].\left| {\bf{V}} \right| = \sqrt {{A^2} + {B^2}}[/tex]

Substitute

[tex]2{x^2}t \ \ for\ A\ and\ 2{x^2}t \ \ for \ B.[/tex]

[tex]\begin{array}{c}\\\left| {\bf{V}} \right| = \sqrt {{{\left( {2{x^2}t} \right)}^2} + {{\left( {2{x^2}t} \right)}^2}} \\\\ = \left( {2\sqrt 2 } \right){x^2}t\\\end{array}[/tex]

The velocity of the fluid particles on the x-axis is [tex]\left( {2\sqrt 2 } \right){x^2}t{\rm{ m/s}}[/tex]

Calculate the direction of flow.

[tex]\theta = {\tan ^{ - 1}}\left( {\frac{B}{A}} )[/tex]

Here, θ is the flow from positive x-axis in a counterclockwise direction.

Substitute [tex]2{x^2}t[/tex] as A and [tex]2{x^2}t[/tex] as B.

[tex]\begin{array}{c}\\\theta = {\tan ^{ - 1}}\left( {\frac{{2{x^2}t}}{{2{x^2}t}}} \right)\\\\ = {\tan ^{ - 1}}\left( 1 \right)\\\\ = 45^\circ \\\end{array}[/tex]

The direction of flow is [tex]45^\circ[/tex] from the positive x-axis.

Question:Technician A say's that The most two-stroke engines have a pressure type lubrication system. Technician be says that four stroke engines do not require the mixing of oil with gasoline . Which of them is correct ?

Answer: Technician  B is   correct

Explanation: Two types of engines exist , the two stroke (example, used in chainsaws)  is a type of engine that uses two strokes--a compression stroke and a return stroke to produce power in a crankshaft combustion cycle and the  four stroke engines(eg lawnmowers) which  uses four strokes,  2-strokes during  compression and exhaustion accompanied by 2 return strokes for each of the initial process to produce power in a combustion cycle.

While a 2 stroke system engine, requires mixing of oil and fuel to the crankshaft before  forcing  the mixture into the cylinder and do not require a pressurized system.  The 4 stroke system uses a splash and pressurized system where oil is not mixed with gasoline but drawn from the sump and  directed to  the main moving  parts of  crankshaft through its channels.

We can therefore say that Technician A is wrong while Technician B is  correct