Answer:
Proved (See Explanation)
Step-by-step explanation:
Show that 3ⁿ⁺⁴ - 3ⁿ is divisible by 16.
This is done as follows
From laws of indices;
aᵐ⁺ⁿ = aᵐ * aⁿ.
So, 3ⁿ⁺⁴ can be written as 3ⁿ * 3⁴.
becomes
Factorize
3ⁿ * 5
5(3ⁿ)
<em>The expression can not be further simplified.</em>
<em>However, we can conclude that when 3ⁿ⁺⁴ - 3ⁿ is divisible by 16, because 5(3ⁿ) is a natural whole number as long as n is a natural whole number.</em>
Step-by-step explanation:
Arithmetic mean
Answer:
b) 29π mm²
Step-by-step explanation:
Answer:
9.8 units
Explanation:
According to Pythagoras theorem, the square of length of the hypotenuse is equal to the sum of squares of lengths of other two sides.
Let the third side be x units.
Then,
x² + 10² = 14²
=> x² + 100 = 196
=> x² = 196 - 100
=> x² = 96
=> x = √96
=> x = 4√6
=> x = 9.79....
=> x = 9.8 (Rounding to the nearest tenths)
So, the length of the third side is 9.8 units.
