Two congruent solids s1 and s2 have the property that s1∩s2 is a right triangular prism with height 3 and a base that is an equilateral triangle of side length 2. if the volume of s1∪s2 is 25 units3, find the volume of s1.

S1=9.905 cubic units

Step-by-step explanation:

As the two solids are congruent it can be said that they have the same angles and the same lengths then their volume is equal and therefore S1= S2 then S1∪S2= S1+S2- S1∩S2 = S1+S1- S1∩S2 =2S1- S1∩S2 =25.

Now, S1∩ S2= Prism volume= (Area of triangle (A)*Height(h)), the area of the equilateral triangle that is the base of the prism is given by A=√3/4*(length Lateral) ^2= A=√3/4*(2^2 )=√3 square units .

Then S1∩ S2=A*h =√3*3=5. 19 cubic units .

Finally you have

2S1- S1∩S2 =25

2S1-5. 19=25 clearing s1 you have

S1=(25-5. 19)/2 = 9. 905 cubic units

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.