Proving a relation for all natural numbers involves proving it for n = 1 and showing that it holds for n + 1 if it is assumed that it is true for any n.
The relation 2+4+6+...+2n = n^2+n has to be proved.
If n = 1, the right hand side is equal to 2*1 = 2 and the left hand side is equal to 1^1 + 1 = 1 + 1 = 2
Assume that the relation holds for any value of n.
2 + 4 + 6 + ... + 2n + 2(n+1) = n^2 + n + 2(n + 1)
= n^2 + n + 2n + 2
= n^2 + 2n + 1 + n + 1
= (n + 1)^2 + (n + 1)
This shows that the given relation is true for n = 1 and if it is assumed to be true for n it is also true for n + 1.
<span>By mathematical induction the relation is true for any value of n.</span>
We are given the bounds of x so after calculation
144 is the answer
Answer:
6.7 seconds
Step-by-step explanation:
Let's calculate the maximum height covered by the object
Max height= U²Sin²tita/2g
Where g is acceleration due to gravity
Max height= 40²(sin90)²/(2*9.81)
Max height= 1600/19.62
Max height=81.55 m
Total max height= 30+81.55
Total max height= 111.55 m
Time t it will take to travel from the max height at acceleration of 4.9 m/s²
S= ut + ½at²
u= 0 at Mac height
S= 111.5 m
111.5 = ½(4.9)t²
223/4.9= t²
45.5= t²
6.745 seconds= t
6.7 seconds= t
Answer:
u can use fraction calculator
Step-by-step explanation:
just go and search 'fraction calculator'
