Step-by-step explanation:
Standard polynomial is:
![- 20 {x}^{3} - 3 {x}^{2} + 4x](https://tex.z-dn.net/?f=%20-%2020%20%7Bx%7D%5E%7B3%7D%20%20-%203%20%7Bx%7D%5E%7B2%7D%20%20%2B%204x)
Leading co effecient is:
-20
Given
- f(n) values for n=1,2,3,4
- possible candidates for the function
Solution:
Method: Evaluate some of the values, for each function. A function with ANY value not matching the given f(n) values will be rejected.
N=1, f(n)=4
f(1)=4-3(1-1)=4
f(1)=4+3^(1+1)=4+3^2=4+9=13 ≠ 4 [rejected]
f(1)=4(3^(n-1))=4(3^0)=4
f(1)=3(4^(n-1))=3(4^0)=3*1=3 [rejected]
N=2, f(n)=12
f(1)=4-3(2-1)=4-3(1)=1 ≠ 12 [rejected]
[rejected]
f(1)=4(3^(2-1)=4*3^1=4*3=12
[rejected]
Will need to check one more to be sure
N=3, f(n)=3
[rejected]
[rejected]
f(3)=4(3^(n-1))=4(3^(3-1))=4(3^2)=4*9=36 [Good]
[rejected]
Solution: f(n)=4(3^(n-1))
Answer:
x = 65
Step-by-step explanation:
using the Altitude- on- Hypotenuse theorem
(leg of big Δ )² = (part of hypotenuse below it ) × (whole hypotenuse)
x² = 25 × 169 = 4225 ( take square root of both sides )
x =
= 65
Greetings from Brasil...
<em />
Here's our problem:
![\large{\frac{12^{16}}{12^{4}}}](https://tex.z-dn.net/?f=%5Clarge%7B%5Cfrac%7B12%5E%7B16%7D%7D%7B12%5E%7B4%7D%7D%7D)
From potentiation properties:
Mᵃ ÷ Mᵇ = Mᵃ⁻ᵇ
<em>division of power of the same base: I repeat the base and subtract the exponents</em>
<em />
Bringing to our problem
12¹⁶ ÷ 12⁴
12¹⁶⁻⁴
<h2>12¹²</h2>