Hello!
To compare the two, we must convert 5/8 to a decimal. We'll do that buy dividing the numerator by the denominator.
5 ÷ 8 = 0.625
Compare the two decimals.
0.625 vs. 0.580
So, 5/8 is obviously bigger than 0.58.
One may note you never quite asked anything, now, assuming simplification,
Functions have one output for every input. So that means one x-coordinate for one y-coordinate. In this case, (3,4) and (3,12) have the same x-coordinate, so it can't be a function.
Answer:
70.45%
Step-by-step explanation:
The markup is $75 -44 = $31. As a percentage of the wholesale price, that is ...
$31/$44 × 100% ≈ 70.45%
Solution :
Along the edge 
The parametric equation for
is given :

Along edge 
The curve here is a quarter circle with the radius 9. Therefore, the parametric equation with the domain
is then given by :


Along edge 
The parametric equation for
is :

Now,
x = 9t, ⇒ dx = 9 dt
y = 0, ⇒ dy = 0

And


Then :

![$=\int_0^1 \left[\left( 9 \sin \frac{\pi}{2}t\right)^2\left(9 \cos \frac{\pi}{2}t\right)\left(-\frac{7 \pi}{2} \sin \frac{\pi}{2}t dt\right) + \left( 9 \cos \frac{\pi}{2}t\right)^2\left(9 \sin \frac{\pi}{2}t\right)\left(\frac{7 \pi}{2} \cos \frac{\pi}{2}t dt\right) \right]$](https://tex.z-dn.net/?f=%24%3D%5Cint_0%5E1%20%5Cleft%5B%5Cleft%28%209%20%5Csin%20%5Cfrac%7B%5Cpi%7D%7B2%7Dt%5Cright%29%5E2%5Cleft%289%20%5Ccos%20%5Cfrac%7B%5Cpi%7D%7B2%7Dt%5Cright%29%5Cleft%28-%5Cfrac%7B7%20%5Cpi%7D%7B2%7D%20%5Csin%20%5Cfrac%7B%5Cpi%7D%7B2%7Dt%20dt%5Cright%29%20%2B%20%5Cleft%28%209%20%5Ccos%20%5Cfrac%7B%5Cpi%7D%7B2%7Dt%5Cright%29%5E2%5Cleft%289%20%5Csin%20%5Cfrac%7B%5Cpi%7D%7B2%7Dt%5Cright%29%5Cleft%28%5Cfrac%7B7%20%5Cpi%7D%7B2%7D%20%5Ccos%20%5Cfrac%7B%5Cpi%7D%7B2%7Dt%20dt%5Cright%29%20%5Cright%5D%24)
![$=\left[-9^4\ \frac{\cos^4\left(\frac{\pi}{2}t\right)}{\frac{\pi}{2}} -9^4\ \frac{\sin^4\left(\frac{\pi}{2}t\right)}{\frac{\pi}{2}} \right]_0^1$](https://tex.z-dn.net/?f=%24%3D%5Cleft%5B-9%5E4%5C%20%5Cfrac%7B%5Ccos%5E4%5Cleft%28%5Cfrac%7B%5Cpi%7D%7B2%7Dt%5Cright%29%7D%7B%5Cfrac%7B%5Cpi%7D%7B2%7D%7D%20-9%5E4%5C%20%5Cfrac%7B%5Csin%5E4%5Cleft%28%5Cfrac%7B%5Cpi%7D%7B2%7Dt%5Cright%29%7D%7B%5Cfrac%7B%5Cpi%7D%7B2%7D%7D%20%5Cright%5D_0%5E1%24)
= 0
And
x = 0, ⇒ dx = 0
y = 9 t, ⇒ dy = 9 dt

Therefore,

= 0 + 0 + 0
Applying the Green's theorem


Here,



Therefore,


The vector field F is =
is conservative.