Hey,
So first we are told that they charg a fixed fee of 25:00 right?That means even if you didn’t send any text messages you still have to pay 25:00.
So first we have to subtract that 25:00 form 58.25 right?This means the rest of the bill is for text messages OK?
So he spent 33.25(this is the answer to the subtraction) on the text messages right?
And for every text he sent he was charged 0.35 right? So we have to divide 33.25 by 0.35 right?
And that gets us 95.
Now we can double check the answer by multiplieng 95 by 0.35 and adding 25.
So th answer is 95
Hope this helps !!
Implicit differentiation
take the deritivive with respect to x
first
y+2=(1/2)(x^2)-2sin(y)
take deritivitive
dy/dx+0=1/2(2x)-2(cosy)dy/dx
dy/dx=x-2cosy(dy/dx)
add 2cosy(dy/dx) to both sides
dy/dx+2cosy(dy/dx) =x
undistribute dy/dx
dy/dx(1+2cos(y))=x
divide both sides by 1+2cos(y)

at (2,0)
x=2
y=0




the slope is 2/3
The lesser one is -4 and the greater x is 0.5
(3x+1) + (2x+8) = 180
5x+9=180
5x=171