N = -3
5n + n + 6 = -18 - 2n
6n + 6 = -18 - 2n
-6 to both sides
6n = -24 - 2n
+2n to both sides
8n = -24
divide 8 to both sides
n = -3
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>
N = 3 is the number of times the coin is tossed. Since there are 2 outcomes per toss, this means that there are 2^n = 2^3 = 2*2*2 = 8 outcomes total. Therefore, there are 8 leaves total.
If we make
H = heads
T = tails
Then here are the 8 outcomes in the sample space
HHH
HHT
HTH
THH
HTT
THT
TTH
TTT
Answer:
113.04
Step-by-step explanation:
formula for area is
pi times radius times radius
if the radius is 6,
do 6 times 6=36
36 times 3.14=113.04
Answer:
-xy^6 +2y -6
Step-by-step explanation:
(-6x^2 y^8+12xy^3-36xy^2)
-------------------------------------------
6xy^2
Divide each term by 6 in the numerator and denominator
(-6/6x^2 y^8+12/6xy^3-36/6xy^2)
-------------------------------------------
6/6xy^2
-x^2y^8 +2xy^3 -6xy^2
---------------------------------
xy^2
Divide each term by x in the numerator and denominator
-x^2/xy^8 +2x/xy^3 -6x/xy^2
---------------------------------
x/xy^2
-xy^8 +2y^3 -6y^2
---------------------------------
y^2
Divide each term by y^2 in the numerator and denominator
Remember when dividing, we subtract the exponents
-xy^8/y^2 +2y^3/y^2 -6y^2/y^2
---------------------------------
y^2 /y^2
-xy^6 +2y^1 -6
---------------------------------
1
-xy^6 +2y -6
