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3 years ago

Please help me

Engineering

1 answer:

Minchanka [31]3 years ago

7 0

Answer:

The first step of the problem solving process is to identify and define the problem. The second step, which is to analyze the problem, involves gathering information, sorting through relevant and irrelevant information, and evaluating the source of the problem by asking the Five W's: who, what, where, when, and why.

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Ayden read 84 pages in 2 hours. At that rate, how many pages can he read in 5 hours

Papessa [141]

Answer:210

Explanation:

Divide 84 by 2 and then multiply by 5 by that number

3 0

4 years ago

Read 2 more answers

A civil engineer is analyzing the compressive strength of concrete. The compressive strength is approximately normal distributed

hram777 [196]

Answer:

See explanation

Explanation:

Solution:-

- A study on compressive strength of a concrete was made. The distribution of compressive strength ( experimental testing ) was normally distributed with variance ( σ^2 ).

- A random sample of n = 12 specimens were taken and the mean compressive strength ( μ ) of 3500 psi was claimed.

- We are to test the claim made by the civil engineer regarding the mean compressive strength of the concrete. The data of compressive strength of each specimen from the sample is given below:

3273, 3229, 3256, 3272, 3201, 3247, 3267, 3237,

3286, 3210, 3265, 3273

- We will conduct the hypothesis whether the mean compressive strength of the concrete conforms to the claimed value.

Null hypothesis: μ = 3500 psi

Alternate hypothesis: μ ≠ 3500 psi

- The type of test performed on the sample data will depend on the application of Central Limit Theorem.

- The theorem states that the sample can be assumed to be normally distributed if drawn from a normally distributed population. ( We are given the population is normally distributed; hence, theorem applies )

- We will approximate the mean of the population ( μ ) with the sample mean ( x ), as per the implication specified by the theorem.

- The mean of the sample ( x ) is calculated as follows:

$x = \frac{Sum ( x_i )}{n} \\\\x = \frac{Sum ( 3273+ 3229+ 3256+ 3272+ 3201+ 3247+ 3267+ 3237+ 3286+ 3210+ 3265+3273 )}{12} \\\\x = \frac{39016}{12} \\\\x = 3251.3333$

- Since, we are testing the average compressive strength of a concrete against a claimed value. Any value that deviates significantly from the claimed value is rejected. This corroborates the use of one sample two tailed test.

- The test value may be evaluated from either z or t distribution. The conditions for z-test are given below:

The population variance is known OR sample size ( n ≥ 30 )

- The population variance is known; hence, we will use z-distribution to evaluate the testing value as follows:

$Z-test = \frac{x - u}{\sqrt{\frac{sigma^2}{n} } } \\\\Z-test = \frac{3251.333 - 3500}{\sqrt{\frac{1000^2}{12} } } \\\\Z-test = -27.24$

- The rejection region for the hypothesis is defined by the significance level ( α = 0.01 ). The Z-critical value ( limiting value for the rejection region ) is determined:

Z-critical = Z_α/2 = Z_0.005

- Use the list of correlation of significance level ( α ) and critical values of Z to determine:

Z-critical = Z_0.005 = ± 2.576

- Compare the Z-test value against the rejection region defined by the Z-critical value.

Rejection region: Z > 2.576 or Z < -2.576

- The Z-test value lies in the rejection region:

Z-test < Z-critical

-27.24 < -2.576 .... Null hypothesis rejected

Conclusion: The claim made by the civil engineer has little or no statistical evidence as per the sample data available; hence, the average compressive strength is not 3500 psi.

- To construct a confidence interval for the mean compressive strength ( μ ) we need to determine the margin of error for the population.

- The margin of error (ME) is defined by the following formula:

$ME = Z^*. \frac{sigma}{\sqrt{n} }$

Where,

- The ( Z* ) is the critical value for the defined confidence level ( CI ):

- The confidence interval and significance level are related and critical value Z* is as such:

α = 1 - CI , Z* = Z_α/2

- The critical values for ( CI = 99% & 95% ) are evaluated:

α = 1 - 0.99 = 0.01 , α = 1 - 0.95 = 0.05

Z* = Z_0.005 , Z* = Z_0.025

Z* = ± 2.58 , Z* = ± 1.96

- The formulation of Confidence interval is given by the following inequality:

[ x - ME < μ < x + ME ]

[ x - Z*√σ^2 / n < μ < x + Z*√σ^2 / n ]

- The CI of 95% yields:

[ 3251.33 - 1.96*√(1000 / 12) < μ < 3251.33 + 1.96*√(1000 / 12) ]

[ 3251.333 - 17.89227 < μ < 3251.33 + 17.89227 ]

[ 3233.44 < μ < 3269.23 ]

- The CI of 99% yields:

[ 3251.33 - 2.58*√(1000 / 12) < μ < 3251.33 + 2.58*√(1000 / 12) ]

[ 3251.333 - 23.552 < μ < 3251.33 + 23.552 ]

[ 3227.78 < μ < 3274.88 ]

- We see that the width of the confidence interval increases as the confidence level ( CI ) increases. This is due to the increase in critical value ( Z* ) associated with the significance level ( α ) increases.

7 0

3 years ago

"Carbon 14 (C-14), a radioactive isotope of carbon, has a half-life of 5730 ± 40 years. Measuring the amount of this isotope lef

igor_vitrenko [27]

Answer:

The age of the bones is approximately 14172 years.

Explanation:

The age of the bones can be determinated using the following decay equation:

$N_{(t)} = N_{0}e^{-\lambda t}$ (1)

<u>Where:</u>

N(t): is the quantity of C-14 at time t

No: is the initial quantity of C-14

λ: is the decay rate

t: is the time

First, we need to find λ:

$\lambda = \frac{ln(2)}{t_{1/2}}$

<u>Where:</u>

t(1/2): is the half-life of C-14 = 5730 y

$\lambda = \frac{ln(2)}{5730 y} = 1.21 \cdot 10^{-04} y^{-1}$

Now, we can calculate the age of the bones by solving equation (1) for t:

$t = \frac{-ln(\frac{N_{(t)}}{N_{0}})}{\lambda}$

We know that the bones have lost 82% of the C-14 they originally contained, so:

$N_{t} = (1 - 0.82)N_{0} = 0.18N_{0}$

$t = \frac{-ln(0.18)}{1.21 \cdot 10^{-04} y^{-1}}$

$t = 14172 y$

Therefore, the age of the bones is approximately 14172 years.

I hope it helps you!

3 0

3 years ago

Air enters a compressor operating at steady state at 1.05 bar, 300 K, with a volumetric flow rate of "84" m3/min and exits at 12

Nina [5.8K]

Answer:

W = - 184.8 kW

Explanation:

Given data:

$P_1 = 1.05 bar$

$T_1 = 300K$

$\dot V_1 = 84 m^3/min$

$P_2 = 12 bar$

$T_2 = 400 K$

We know that work is done as

$W = - [ Q + \dor m[h_2 - h_1]]$

for $P_1 = 1.05 bar, T_1 = 300K$

density of air is 1.22 kg/m^3 and $h_1 = 300 kJ/kg$

for $P_2 = 12 bar, T_2 = 400 K$

$h_2 = 400 kj/kg$

$\dot m = \rho \times \dor v_1 = 1.22 \frac{84}{60} =1.708 kg/s$

W = -[14 + 1.708[400-300]]

W = - 184.8 kW

8 0

3 years ago

A shaft made of stainless steel has an outside diameter of 42 mm and a wall thickness of 4 mm. Determine the maximum torque T th

fiasKO [112]

Answer:

Explanation:

Using equation of pure torsion

$\frac{T}{I_{polar} }=\frac{t}{r}$

where

T is the applied Torque

$I_{polar}$ is polar moment of inertia of the shaft

t is the shear stress at a distance r from the center

r is distance from center

For a shaft with

$D_{0} =$ Outer Diameter

$D_{i} =$ Inner Diameter

$I_{polar}=\frac{\pi (D_{o} ^{4}-D_{in} ^{4}) }{32}$

Applying values in the above equation we get

$I_{polar} =\frac{\pi(0.042^{4}-(0.042-.008)^{4})}{32}\\I_{polar}= 1.74$ x $10^{-7} m^{4}$

Thus from the equation of torsion we get

$T=\frac{I_{polar} t}{r}$

Applying values we get

$T=\frac{1.74X10^{-7}X100X10^{6} }{.021}$

T =829.97Nm

7 0

3 years ago