Answer:
Step-by-step explanation:
I assume you mean 
:
Use the formula 
where 
and 
are the lower and upper bounds and 
is the equation of the polar curve.
Since the graph is symmetrical about the line 
, let the bounds of integration be 
to find half the area of the curve, and then find twice of that area:
![A=\biggr[41\biggr(\frac{\pi}{2}\biggr)-48\cos\biggr(\frac{\pi}{2}\biggr)-16\sin2\biggr(\frac{\pi}{2}\biggr)\biggr]-\biggr[41\biggr(-\frac{\pi}{2}\biggr)-48\cos\biggr(-\frac{\pi}{2}\biggr)-16\sin2\biggr(-\frac{\pi}{2}\biggr)\biggr]\\\\A=\biggr[\frac{41\pi}{2}-24\sqrt{2}\biggr]-\biggr[-\frac{41\pi}{2}+24\sqrt{2}\biggr]\\ \\A=41\pi\\\\A\approx128.8053](https://tex.z-dn.net/?f=A%3D%5Cbiggr%5B41%5Cbiggr%28%5Cfrac%7B%5Cpi%7D%7B2%7D%5Cbiggr%29-48%5Ccos%5Cbiggr%28%5Cfrac%7B%5Cpi%7D%7B2%7D%5Cbiggr%29-16%5Csin2%5Cbiggr%28%5Cfrac%7B%5Cpi%7D%7B2%7D%5Cbiggr%29%5Cbiggr%5D-%5Cbiggr%5B41%5Cbiggr%28-%5Cfrac%7B%5Cpi%7D%7B2%7D%5Cbiggr%29-48%5Ccos%5Cbiggr%28-%5Cfrac%7B%5Cpi%7D%7B2%7D%5Cbiggr%29-16%5Csin2%5Cbiggr%28-%5Cfrac%7B%5Cpi%7D%7B2%7D%5Cbiggr%29%5Cbiggr%5D%5C%5C%5C%5CA%3D%5Cbiggr%5B%5Cfrac%7B41%5Cpi%7D%7B2%7D-24%5Csqrt%7B2%7D%5Cbiggr%5D-%5Cbiggr%5B-%5Cfrac%7B41%5Cpi%7D%7B2%7D%2B24%5Csqrt%7B2%7D%5Cbiggr%5D%5C%5C%20%5C%5CA%3D41%5Cpi%5C%5C%5C%5CA%5Capprox128.8053)
Thus, the area of the curve is 41π square units. See below for a graph of the curve and its shaded area.
Answer:
she bought 4 braclets
Step-by-step explanation:
if you do 20 times 4 it gets you 80 and if you subtract 50 it leaves you with 30 meaning she bought 4 bracelets
i do hope this helps even tho my explanation isn't exactly the best
Answer:
1.5
Step-by-step explanation:
If 1 tablet is 100mg, and you need 150mg, we set up this equation:
Let x be the number of tablets Coco needs.
x = 150/100
x = 1.5
Therefore, you need 1.5 tablets for the medication.
5 students. 15 + 30 is 45, so the remainder is 5
Answer:
One piece is 23.5
the other is 41.5
Step-by-step explanation:
first subtract 18 from 65 that will give you 47. Then 47÷2= 23.5. this is the length of the shorter piece. since one piece is 18 m longer then the other, add 18 to 23.5. that will give you the length of the longer piece. You can check your work by adding 23.5 and 41.5. They equal 65.
