How many of the first 80 positive integers can he written as the sum of two distinct powers of 3? for example, 28=27+1=3^3+3^0 can be expressed, but 29 cannot be.

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Ответ:

Zhodges5020

07.04.2023

Mathematics

$\huge\boxed{A=6x^2-11x+3;\ \text{for}\ x1.5}$

Step-by-step explanation:

The formula of an area of a rectangle:

$A=a\cdot b\\\\a,\ b-\text{sides of a rectangle}$

We have:

$a=2x-3\\b=3x-1$

The domain:

$2x-30\ \wedge\ 3x-10\\\\2x-3+30+3\ \wedge\ 3x-1+10+1\\\\2x3\ \wedge\ 3x1\\\\\dfrac{2x}{2}\dfrac{3}{2}\ \wedge\ \dfrac{3x}{3}\dfrac{1}{3}\\\\x1.5\ \wedge\ x\dfrac{1}{3}\Rightarrow\boxed{x1.5}$

Substitute:

A=(2x-3)(3x-1)

use FOIL: (a + b)(c + d) = ac + ad + bc + bd

$A= (2x)(3x)+(2x)(-1)+(-3)(3x)+(-3)(-1)\\\\A=6x^2-2x-9x+3$

combine like terms

$A= 6x^2+(-2x-9x)+3\\\\A=6x^2-11x+3$

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