Answer:
isosceles triangle
Step-by-step explanation:
It looks like you want to compute the double integral
![\displaystyle \iint_D (x+y) \,\mathrm dx\,\mathrm dy](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ciint_D%20%28x%2By%29%20%5C%2C%5Cmathrm%20dx%5C%2C%5Cmathrm%20dy)
over the region <em>D</em> with the unit circle <em>x</em> ² + <em>y</em> ² = 1 as its boundary.
Convert to polar coordinates, in which <em>D</em> is given by the set
<em>D</em> = {(<em>r</em>, <em>θ</em>) : 0 ≤ <em>r</em> ≤ 1 and 0 ≤ <em>θ</em> ≤ 2<em>π</em>}
and
<em>x</em> = <em>r</em> cos(<em>θ</em>)
<em>y</em> = <em>r</em> sin(<em>θ</em>)
d<em>x</em> d<em>y</em> = <em>r</em> d<em>r</em> d<em>θ</em>
Then the integral is
![\displaystyle \iint_D (x+y)\,\mathrm dx\,\mathrm dy = \iint_D r^2(\cos(\theta)+\sin(\theta))\,\mathrm dr\,\mathrm d\theta \\\\ = \int_0^{2\pi} \int_0^1 r^2(\cos(\theta)+\sin(\theta))\,\mathrm dr\,\mathrm d\theta \\\\ = \underbrace{\left( \int_0^{2\pi}(\cos(\theta)+\sin(\theta))\,\mathrm d\theta \right)}_{\int = 0} \left( \int_0^1 r^2\,\mathrm dr \right) = \boxed{0}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ciint_D%20%28x%2By%29%5C%2C%5Cmathrm%20dx%5C%2C%5Cmathrm%20dy%20%3D%20%5Ciint_D%20r%5E2%28%5Ccos%28%5Ctheta%29%2B%5Csin%28%5Ctheta%29%29%5C%2C%5Cmathrm%20dr%5C%2C%5Cmathrm%20d%5Ctheta%20%5C%5C%5C%5C%20%3D%20%5Cint_0%5E%7B2%5Cpi%7D%20%5Cint_0%5E1%20r%5E2%28%5Ccos%28%5Ctheta%29%2B%5Csin%28%5Ctheta%29%29%5C%2C%5Cmathrm%20dr%5C%2C%5Cmathrm%20d%5Ctheta%20%5C%5C%5C%5C%20%3D%20%5Cunderbrace%7B%5Cleft%28%20%5Cint_0%5E%7B2%5Cpi%7D%28%5Ccos%28%5Ctheta%29%2B%5Csin%28%5Ctheta%29%29%5C%2C%5Cmathrm%20d%5Ctheta%20%5Cright%29%7D_%7B%5Cint%20%3D%200%7D%20%5Cleft%28%20%5Cint_0%5E1%20r%5E2%5C%2C%5Cmathrm%20dr%20%5Cright%29%20%3D%20%5Cboxed%7B0%7D)
"y>-2x+2 and y>-2x+5" are illustrated graphically by 2 straight dashed lines with slope -2. The lines are parallel because their slopes (-2) are the same. One line has y intercept 2 and the other has y intercept 5. The latter is above the former. Since both inequality signs are " > " we must shade the area ABOVE each of the 2 lines. The solution set is the area of the graph that has been shaded twice, once for y>-2x+2 and again for y>-2x+5. It's y>-2x+5 that has been shaded twice; this area is immediately above the line y>-2x+5.
From 145 pounds to 132 pounds
145 - 132 = 13
13 pounds
Check:-
132 + 13 = 145
Correct!
13 pounds
So if x people were surveyed,
![\frac{7}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B7%7D%7B8%7D%20)
people owned a bike and
![\frac{1}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B8%7D%20)
did not.
The difference between them is 72:
![\frac{7}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B7%7D%7B8%7D%20)
x-\frac{1}{8} [/tex] =72
so this means that
![\frac{6}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B6%7D%7B8%7D%20)
x=72
let's simplify:
![\frac{3}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B4%7D%20)
x=72
and divide by 3:
![\frac{1}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B4%7D%20)
x=24
and mupliply by 4:
x=96
so 96 people were surveyed