Let p= sin t i + cost j + tk, What is |dp/dt|?
a.\\(\\sqrt(7)\\)
b.\\(\\sqrt(2)\\)
c.\\(\\sqrt(3)\\)
d.\\(\\sqrt(5)\\)

6 x =36?

Quebec is the only province in Canada where the one official language is French. According to a recent census, 79.7% of Quebec residents identify French as their mother tongue. You select an SRS of 165 Quebec residents. What is the probability that less than 80% of them identify French as their mother tongue? (Identify the mean, standard deviation, justification that the large counts condition is met, z-score, and probability).

Explain sexagesimal system used for operations on time. Give one example each of the problems involving subtraction and addition of time showing the error children make because of the sexagesimal system. How would you help children correct their error.

Consider arterial blood viscosity µ = .0 025 poise. If the length of the artery is 5.1 cm, radius
3
8 10−
× cm. and 3
1 2 P = P − P = 4×10 dynes/ 2
cm then find (i) maximum peak velocity of
blood and (ii) the shear stress at the wall.

Give one example each, with justification, to support the following statements. (6)
i) For developing mathematical ability, children should pose problems and not
merely answer them
ii) Children know some mathematics before they enter formal school.
iii) Children learn by experiencing things.

The huge volcanic eruption on the island of Krakatoa, Indonesia, in 1883 was heard on Rodrigues Island, 4,782 km (2,970 miles) away. How long did it take the sound to travel to Rodrigues? (Assume the air temperature is 20°C.)

Bureau of labor statistics wants to use statistics to determine whether there is difference between two countries on some measure of labor or between time periods for one country. The bureau reports that hourly compensation rates in US dollars for manufacturing production workers in country ‘A’ in 2015 and 2019 were $25.96 and $28.29 respectively. Hourly compensation rates for country ‘B’ over same period of time were $19.26 in 1995 and $23.89 in 2004. According to the survey by labor department the hours actually worked by employees per week in country A in 2015 were 36.1 and were 35.5 in 2019. For country B the figures were 37.1 in 2015 and 35.9 in 2019.
ii. How will you help the department statistically to find whether the difference between the two countries’ average workweek is significant or not?(7marks)

in the olden days, type was set by hand using lead pieces. the type had to be carefully put together. the printer wants to print a list of whole numbers from 1 to 1,000 in order to find the primes under 1,000. if he had 100 of each of the digits from 0 to 9 , how many numbers could he set before he ran out of some digits?