Unfortunately, Katie will be $20 short
She has $40
Plus the $38 x 5 she will be earning which is $190
$190+$40 is $230
Looks like Kate needs one more day of hard work to get her bike ; )
N•2>8
then dive both sides 2n>8
and get n>4
Answer:

Step-by-step explanation:
The given differential equation is 
The characteristics equation is given by

Finding the values of r

We got a repeated roots. Hence, the solution of the differential equation is given by

On differentiating, we get

Apply the initial condition y (0)= 3 in equation (i)

Now, apply the initial condition y' (0)= 13 in equation (ii)

Therefore, the solution of the differential equation is

(x-3)(3x+7)=0
x-3=0 or 3x+7=0
1. x-3=0
x₁=3
2. 3x+7=0
3x=-7
x₂=-7/3 = -2(1/3)