424 



PRACTICAL MATHEMATICS 



(10) The following values are taken from the table of cube roots: 



6-1 6-2 6-3 6-4 6-5 6-6 6-7 



1-827160 1-837091 1-846915 1-856636 1-866256 1-875777 1-885204 



Denoting ^6-3 as U Q , find the value of ^6-36. Also, denoting 

 ty&l as u , find the value of ^6-36. 



(11) The following values are taken from the table of tangents : 



60 61 62 63 64 65 66 67 



1-7321 1-8040 1-8807 1-9626 2-0503 2-1445 2-2460 2-3559 



Denoting tan 61 as u , find the value of tan 61 24'. Also, denot- 

 ing tan 66 as U Q , find the value of tan 65 48'. 



(12) From the given table of values of x and y, find the best 



dii 



value of - when x = 0-95. 

 ax 



0-8 

 0-7174 



0-85 

 0-7513 



0-9 

 0-7833* 



0-95 

 0-8134 



1-0 



0-8415 



1-05 



0-8674 



M 



0-8912 



dp 



(13) The following values of p and being given, find -^ when 



e = ii5. 





 p 



100 105 110 115 120 125 130 

 14-70 17-53 20-80 24-54 28-83 33-71 39-25 



(B. of E., 1905.) 



(14) The following values of x and y being given, find the most 



dti 

 probable value of -j- when x is 3. 



a:01 23456 



y 11-8 16-0 20-0 23-9 27-6 31-1 34-5 



(B. of E., 1906.) 



(15) If L = ct ~ where L is latent heat (in foot-pounds), t is 



(ftp 



absolute temperature centigrade, p is pressure in pounds per 

 square foot, c cubic feet is increase of volume if 1 Ib. changes 

 from lower to higher state. Calculate c at t = 428, if the following 

 numbers are given for steam. When t = 428, L is 497-2 x 1393. 



t 413 418 423 428 433 438 443 



p 7563 8698 9966 11380 12940 14680 16580 



(B. of E., 1907.) 

 j 



(16) The following table of values of x and y is given. 



when x = 3. (B. of E., 1913.) 



x 1 23 4 5 



y 6-98970 7-40363 7-78151 8-12913 8-45098 8-75061 9-03090 



