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A single force acts on a 0.71 kg particle-like object in such a way that the position of the object as a function of time is given by $x = 2.1t - 2.4t^2 + 3.4t^3$, with x in meters and t in seconds. Find the work done on the object by the force from t = 0 to t = 6.1 s. Number i Units

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Identify an industrial application in which an electric motor has to drive a load at a constant speed.

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Full marks: 30 marks Show your calculation. Correct your answer to 4 decimal places when applicable. Question 1 (15 marks) In a cinema, the probability distribution function of the number of tickets to be bought by a customer in a single purchase (X) is shown in the following table. x 1 2 3 4 5 6 $P(X = x)$ 0.15 0.35 0.3 $2k$ $k$ $k$ (a) Find the value of $k$. (b) Calculate the expectation, variance and standard deviation of $X$. (c) If it costs $95 per ticket and $10 service charge per purchase, express the total cost per purchase of a customer in terms of $X$. Hence, calculate the expectation, variance and standard deviation of the total cost per purchase of a customer using the results in (b). Question 2 (15 marks) From previous records, the technical support department of a software house replied 85% of all email inquiries within 2 days. Records of 25 email inquiries are randomly chosen. (a) What is the probability that at most 23 email inquiries are replied within 2 days? (b) Calculate the expected value, variance and standard deviation of the number of email inquiries out of 25 inquiries which are replied within 2 days. (c) Using the results in (b) to determine the most likely number of email inquiries out of 25 inquiries which are replied within 2 days. *** END ***

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How many moles of Ar atoms are in 24.9 grams of Ar

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Since potential difference is the energy per unit charge, it is measured in units of energy divided by charge. Specifically, potential difference is generally measured in volts (whose symbol is V ). OThere is a 12 V potential difference between the positive and negative ends of the jumper cables, which are a short distance apart. An electron at the negative end ready to jump to the positive end has a certain amount of potential energy. On what quantities does this electrical potential energy depend?

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Traditionally, zoologists have placed birds in their own class, Aves. More recently, molecular evidence has shown that birds are more closely related to reptiles than their anatomy reveals. Genetically, birds are more closely related to crocodiles than crocodiles are to turtles. Thus, bird anatomy has become highly modified as they have adapted to flight, without their genes having undergone nearly as much change. Taxonomically, what should be done with the birds? (3 points)The rest of the reptiles should be reclassified as a subclass within the class Aves.Birds should be reclassified, and their new taxon should be the subclass Aves. Genetic similarity trumps morphological dissimilarity in cases where morphological traits are uninformative.The classification scheme should remain the same because of historical precedence.The traditional stance is correct. Such dramatic morphological change as undergone by birds indicates that birds should be placed in their own order, separate from the reptiles.

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$p^2(16p^4q^8)^{1/2}=$

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classroom environment: outline a plan to create a surppotive and inclusive classroom environment.

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01. A hexagonal prism, base edge \( 20 \mathrm{~mm} \) and height \( 50 \mathrm{~mm} \), is resting on an edge of its base on HP in such way that the base makes an angle of \( 45^{\circ} \) with the HP. Draw the projection of the prism.

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3. Given the following function. $f(x) = \begin{cases} 1, & -1 \le x < 0 \\ x, & x = 0 \\ 1 - 2x, & 0 < x \le 1 \end{cases}$ on [-1,1] (i) Determine the period of $f(x)$. (ii) Find the Fourier series of $f(x)$. (iii) Show that $\frac{\pi^2}{8} = 1 + \frac{1}{3^2} + \frac{1}{5^2} + ...$

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