Right now the dirt bike is worth $500. Next year it will be worth 15% less, or 85% of the current value (because currently it's at 100%, so you would subtract the 15%). To find 85% of the dirt bike's value, you would take $500 and multiply by 85% (or 0.85). This would give you $425 after 1 year. You'd take $425 and multiply that by 85% for the next year, and continue until you reached 5 years of the value decreasing. Does this help?
As we travel from (-2, p) to (2, 2p+1), x increases by 4 and y increases by p+1. Note that -2 + 4 = 2 (which is correct), and that p + (p+1) = 2p+1 (which is also correct).
p+1
Thus, the slope of this line is m = rise / run = -------- = 9
4
Then p + 1 = 36, and p = 35.
Answer:
x = ± 12
Step-by-step explanation:
Given
f(x) = x² - 144
To find the roots set f(x) = 0, that is
x² - 144 = 0 ( add 144 to both sides )
x² = 144 ( take the square root of both sides )
x = ±
= ± 12
Answer:
The functions satisfy the differential equation and linearly independent since W(x)≠0
Therefore the general solution is

Step-by-step explanation:
Given equation is

This Euler Cauchy type differential equation.
So, we can let

Differentiate with respect to x

Again differentiate with respect to x

Putting the value of y, y' and y'' in the differential equation



⇒m²-10m +24=0
⇒m²-6m -4m+24=0
⇒m(m-6)-4(m-6)=0
⇒(m-6)(m-4)=0
⇒m = 6,4
Therefore the auxiliary equation has two distinct and unequal root.
The general solution of this equation is

and

First we compute the Wronskian


=x⁴×6x⁵- x⁶×4x³
=6x⁹-4x⁹
=2x⁹
≠0
The functions satisfy the differential equation and linearly independent since W(x)≠0
Therefore the general solution is
