Add 15 to both sides to get 6x+22=8x then subtract 6x from both sides to get 22=2x then divide both sides by 2.
X=11
Answer:
(-2,0)
Step-by-step explanation:
Answer: 0.1666
Step-by-step explanation: To find the probability of an event, you divide the number of favorable events by the number of total events. Since there are 6 total events, and rolling a 4 counts as 1 event, you would divide 1 by 6.
1/6 = 0.1666
I Believe The Answer Is 5 . Because 5 Times 3 Is 15 . And 15 + 2 Is 17 .
![y=\displaystyle\int_1^x\sqrt{t^3-1}\,\mathrm dt](https://tex.z-dn.net/?f=y%3D%5Cdisplaystyle%5Cint_1%5Ex%5Csqrt%7Bt%5E3-1%7D%5C%2C%5Cmathrm%20dt)
By the fundamental theorem of calculus,
![\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm d}{\mathrm dx}\displaystyle\int_1^x\sqrt{t^3-1}\,\mathrm dt=\sqrt{x^3-1}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%3D%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cdisplaystyle%5Cint_1%5Ex%5Csqrt%7Bt%5E3-1%7D%5C%2C%5Cmathrm%20dt%3D%5Csqrt%7Bx%5E3-1%7D)
Now the arc length over an arbitrary interval
![(a,b)](https://tex.z-dn.net/?f=%28a%2Cb%29)
is
![\displaystyle\int_a^b\sqrt{1+\left(\frac{\mathrm dy}{\mathrm dx}\right)^2}\,\mathrm dx=\int_a^b\sqrt{1+x^3-1}\,\mathrm dx=\int_a^bx^{3/2}\,\mathrm dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_a%5Eb%5Csqrt%7B1%2B%5Cleft%28%5Cfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%5Cright%29%5E2%7D%5C%2C%5Cmathrm%20dx%3D%5Cint_a%5Eb%5Csqrt%7B1%2Bx%5E3-1%7D%5C%2C%5Cmathrm%20dx%3D%5Cint_a%5Ebx%5E%7B3%2F2%7D%5C%2C%5Cmathrm%20dx)
But before we compute the integral, first we need to make sure the integrand exists over it.
![x^{3/2}](https://tex.z-dn.net/?f=x%5E%7B3%2F2%7D)
is undefined if
![x](https://tex.z-dn.net/?f=x%3C0)
, so we assume
![a\ge0](https://tex.z-dn.net/?f=a%5Cge0)
and for convenience that
![a](https://tex.z-dn.net/?f=a%3Cb)
. Then