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A cantilever of length 2 m carries two point loads of 20 KN at the free end and 30 KN at a distance of 1 m from the free end. Find the slope and deflection at free end. Take E= 2×10^5 N/mm^2 and I= 1.5×10^8 mm^4

A beam of uniform rectangular section 100 mm wide and 240 mm deep is simply supported at its ends. It carries a uniformly distributed load of 9.125 KN/m run over the entire span of 4m. Find the deflection at the centre of E= 1.1×10^4 N/mm^2

The heights of 100 students are normally distributed with a mean height of 16 centimeters and



standard deviation of 5.9 centimeters. Answer the following in percent form.



a. How many of these students would you expect to have heights less than 167 centimeters?



b. How many of these students would you expect to have heights greater than 153 centimeters?



c. How many of these students would you expect to have heights between 150 and 165



centimeters?



d. Find the area of items a, b and c.



e. Compute for the 75th Percentile.

PtCl2(NH3)2

An element with mass 630 grams decays by 18.8% per minute. How much of the element is remaining after 7 minutes, to the nearest 10th of a gram?



(a) Figure 33-27 shows light reaching a polarizing sheet whose

polarizing direction is parallel to a y axis. We shall rotate the sheet 40°

clockwise about the light’s indicated line of travel. During this

rotation, does the fraction of the initial light intensity passed by the

sheet increase, decrease, or remain the same if the light is (a) initially

unpolarized, (b) initially polarized parallel to the x axis, and (c)

initially polarized parallel to the y axis?


Let P(x) be the statement “x spends more than five hours every weekday in class,” where the




domain for x consists of all students. Express each of these quantifications in English.




a) ∃𝑥𝑃(𝑥)




b) ∀𝑥𝑃(𝑥)




c) ∃𝑥¬𝑃(𝑥)




d) ∀𝑥¬𝑃(𝑥)

If the magnetic field of a light wave oscillates parallel to a y axis and is given by By = Bm sin(k z − ωt), (a) in what direction does the wave travel and (b) parallel to which axis does


the associated electric field oscillate?


A box contains 6 red balls, 5 blue balls, and 10 green bas. In how many ways can you choose 2 red balls and 5 green balls



Discuss the properties of isoquant curves.


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