A. Terms
b. 9
64 to 49 is -15, 49 to 36 is -13, 36 to 25 is -11, 25 to 16 is -9, so the next number is 16-7=9
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>
Answer:
I can get you jump started a bit.
Step-by-step explanation:
So Each of those pairs of figures are Similar.
This means they have equal angle measures but different side lengths.
To find it, we have to make a <u>Proportion:</u>
<u>Example: #11</u>
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So let's solve the first one!
Easy As Pie!
If you need more help, contact me! :)
Hope this Helps!
P.S. Stay Safe!
Answer:
a.114.4kg
b. 486kg
Step-by-step explanation:
Firstly , we want to know the value with which the apples weigh more than the oranges
To calculate this, we simply subtract the weight of the oranges from that of the apple
Mathematically, that would be ;
300.2-185.8 = 114.4kg
The total weight of the things bought is calculated by adding both weights together
That would be 185.8 + 300.2 = 486 kg
