Find a set of solutions: Integrating Factors found by Inspection. 1. y(2xy + 1)dx - xdy = 0
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Find a set of solutions: Integrating Factors found by Inspection.
1. y(2xy + 1)dx - xdy = 0
2. y(x+ - y2)dx + x (x + y2)dy = 0
3. (x*y3 + 1)dx + x*y?dy 0
4. y(x?y? - 1)dx + x(x²y2 + 1)dy = 0
5. y(2x + y?)dx + x(y2 - x)dy = 0
6. y(3x - x + y)dx + x2(1- x2)dy = 0
7. y(3x3 – x + y)dx + x(1-x2)dy = 0
8.y?(1 - x)dx + x(x+y + 2x + y) = 0
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- Both bias errors and precision errors can propagate. TRUE OR FLASE(a) A very important component of a system has a mean time between failures of 100 hr and a mean time to repair of 10 hr. Determine the inherent availability of the system. (b) If the equipment in Q7 (c i) above is required to meet an inherent availability requirement of 0.985 and a mean time between failures of 100 hr. Calculate the permissible mean time to repair and if the system as a mean of the time intervals between corrective maintenance actions of 900 hrs and the sum of the mean corrective maintenance time intervals including supply downtime and administrative down time of 10 hrs Determine the operational availability of the systemDo the two analytical methods provide results that are significantly different at the 95% confidence interval? Justify fully, showing all calculations, logic etc
- n a certain dynamic measurement application the input(x) – output(y) relationship is given by y=1+(1+x)e^(-x) With what uncertainty must x be determined to yield a relative uncertainty of ±5 percent for y at a value of x = 2,4In a Measurement ,the Expected value is 94 V and the measured value is 88 V. Find (i) absolute error Ea , (ii)Relative error Er, (iii) Absolute accuracy Aa (iv) Relative Accuracy Ar.The length of a iron bar is measured by a number of different observers and the following set of 12measurements are recorded (units mm)302,304,303,305,307,309,310,311,312,301,303,302. Find the values of mean, median, variance andstandard deviation.
- can you give the uncertainty for these numbers and the rules you follow to find them13.70mm16.40mm0.4965kg0.21m0.499.6kg0.15m0.4993kg0.095m0.4953kg0.057m0.492kg0.049mState whether the following statements true or false 1. The type I error and type II error are related. A decrease in the probability of one generally results in an increase in the probability of the other. 2. The size of the critical region, and therefore the probability of committing a type I error, can always be reduced by adjusting the critical value(s). 3. An increase in the sample size n will reduce α and β simultaneously. 4. If the null hypothesis is false, β is a maximum when the true value of a parameter approaches the hypothesized value. The greater the distance between the true value and the hypothesized value, the smaller β will be. 5. The power of a test is the probability of rejecting H0 given that a specific alternative is true.In a linear spring finite element model, as per the finite element model’s sign convention, which one of the following statements is true? Select one: a. If Fe1 is negative then the spring is under compression b. If Fe2 is negative then the spring is under tension c. If Fe1 is positive then the spring is under tension d. If Fe2 is positive then the spring is under tension
- Pressure distribution measurements are made on a two-dimensional wing model placed in a wind tunnel. The difference between the static pressure sockets on the surface and the static pressure of the free stream is measured. 30 data is taken at each measurement point. The average of the values measured from one of the sockets near the trailing edge was calculated as 2.30 Pa, and the standard deviation was calculated as 2.65 Pa. After applying the Chauvenet criterion to these measurement values, it was decided to eliminate 3 measurements and the new mean value was found to be 2.18 Pa and the standard deviation was 2.42. It was verified that the unexcluded data fit the normal distribution curve. Data above how many Pa and below how many Pa were eliminated? Estimate how many data have negative value (?<0) after elimination.Bearing used in an automotive application has a nominal inside diameter of 3.81 is expected to be cm.A random sample of 25 bearings is selected andaverage inner diameter of bearing3.8037 cm. exists as. bearing inner diameter σ=0.03 cm Standard deviation ofis known to be normally distributed. α=0.01 ; a) Test whether the bearing used has a nominal inside diameter of 3.81 cm. b) How to answer the question in part (a) by constructing a two-sided confidence interval on the mean diameter?explain that you can answer note: can you write the solutions legibly.Give a definition for each term: standard deviation, calibration, uncertainty.