10 A solid metallic cylinder of radius 14 cm and height 21 cm is melted and recast into equal
small spheres each of radius 7/2 cm. Find then
number of spheres formed.

72 spheres are formed

Step-by-step explanation:

We start by calculating the volume of the metallic cylinder

Mathematically, we have this as;

V = pi * r^2 * h

V = pi * 21 * 14^2

V = 4116 π cm^3

The volume of each small sphere is;

V = 4/3 * pi * r^3

= 4/3 * π * 7/2^3 = 57.167 π cm^3

To get the number of small spheres, we simply divide the volumes

That will be 4116 pi / 57.167 pi = 72

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47