Answer:
Speed= Dist/time= p/x miles per minuteTime to run q miles=q divided by p/x= qx/p minutes
Answer:
-4/5 = x
Step-by-step explanation:
Rewrite the boundary lines <em>y</em> = -1 - <em>x</em> and <em>y</em> = <em>x</em> - 1 as functions of <em>y </em>:
<em>y</em> = -1 - <em>x</em> ==> <em>x</em> = -1 - <em>y</em>
<em>y</em> = <em>x</em> - 1 ==> <em>x</em> = 1 + <em>y</em>
So if we let <em>x</em> range between these two lines, we need to let <em>y</em> vary between the point where these lines intersect, and the line <em>y</em> = 1.
This means the area is given by the integral,
![\displaystyle\iint_T\mathrm dA=\int_{-1}^1\int_{-1-y}^{1+y}\mathrm dx\,\mathrm dy](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciint_T%5Cmathrm%20dA%3D%5Cint_%7B-1%7D%5E1%5Cint_%7B-1-y%7D%5E%7B1%2By%7D%5Cmathrm%20dx%5C%2C%5Cmathrm%20dy)
The integral with respect to <em>x</em> is trivial:
![\displaystyle\int_{-1}^1\int_{-1-y}^{1+y}\mathrm dx\,\mathrm dy=\int_{-1}^1x\bigg|_{-1-y}^{1+y}\,\mathrm dy=\int_{-1}^1(1+y)-(-1-y)\,\mathrm dy=2\int_{-1}^1(1+y)\,\mathrm dy](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_%7B-1%7D%5E1%5Cint_%7B-1-y%7D%5E%7B1%2By%7D%5Cmathrm%20dx%5C%2C%5Cmathrm%20dy%3D%5Cint_%7B-1%7D%5E1x%5Cbigg%7C_%7B-1-y%7D%5E%7B1%2By%7D%5C%2C%5Cmathrm%20dy%3D%5Cint_%7B-1%7D%5E1%281%2By%29-%28-1-y%29%5C%2C%5Cmathrm%20dy%3D2%5Cint_%7B-1%7D%5E1%281%2By%29%5C%2C%5Cmathrm%20dy)
For the remaining integral, integrate term-by-term to get
![\displaystyle2\int_{-1}^1(1+y)\,\mathrm dy=2\left(y+\frac{y^2}2\right)\bigg|_{-1}^1=2\left(1+\frac12\right)-2\left(-1+\frac12\right)=\boxed{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle2%5Cint_%7B-1%7D%5E1%281%2By%29%5C%2C%5Cmathrm%20dy%3D2%5Cleft%28y%2B%5Cfrac%7By%5E2%7D2%5Cright%29%5Cbigg%7C_%7B-1%7D%5E1%3D2%5Cleft%281%2B%5Cfrac12%5Cright%29-2%5Cleft%28-1%2B%5Cfrac12%5Cright%29%3D%5Cboxed%7B4%7D)
Alternatively, the triangle can be said to have a base of length 4 (the distance from (-2, 1) to (2, 1)) and a height of length 2 (the distance from the line <em>y</em> = 1 and (0, -1)), so its area is 1/2*4*2 = 4.
Answer:
y=(-7x+3)/8
Step-by-step explanation:
8y=-7x+3
y=(-7x+3)/8