Assuming these are 4^(1/7), 4^(7/2), 7^(1/4) and 7^(1/2), the conversion process is pretty quick. the denominator, or bottom, of your fraction exponent becomes the "index" of your radical -- in ∛, "3" is your index, just for reference. the numerator, aka the top of the fraction exponent, becomes a power inside the radical.
4^(1/7) would become ⁷√4 .... the bottom of the fraction becomes the small number included in the radical and the 4 goes beneath the radical
in cases such as this one, where 1 is on top of the fraction radical, that number does technically go with the 4 beneath the radical--however, 4¹ = 4 itself, so there is no need to write the implied exponent.
4^(7/2) would become √(4⁷) ... the 7th power goes with the number under your radical and the "2" becomes a square root
7^(1/4) would become ⁴√7 ... like the first answer, the bottom of the fraction exponent becomes the index of the radical and 7 goes beneath the radical. again, the 1 exponent goes with the 7 beneath the radical, but 7¹ = 7
7^(1/2) would become, simply, √7
Answer:
I believe the radius is half the circle which makes the diameter 2x the radius which is 35+35= 70
Answer:
Answer is 1
Explanation:
(-6 + 5) / (-2 + 1)
-1 / -1
1
tis noteworthy that the segment contains endpoints of A and C and the point B is in between A and C cutting the segment in a 1:2 ratio,
![\bf \textit{internal division of a line segment using ratios} \\\\\\ A(-9,-7)\qquad C(x,y)\qquad \qquad \stackrel{\textit{ratio from A to C}}{1:2} \\\\\\ \cfrac{A\underline{B}}{\underline{B} C} = \cfrac{1}{2}\implies \cfrac{A}{C}=\cfrac{1}{2}\implies 2A=1C\implies 2(-9,-7)=1(x,y)\\\\[-0.35em] ~\dotfill\\\\ B=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Binternal%20division%20of%20a%20line%20segment%20using%20ratios%7D%20%5C%5C%5C%5C%5C%5C%20A%28-9%2C-7%29%5Cqquad%20C%28x%2Cy%29%5Cqquad%20%5Cqquad%20%5Cstackrel%7B%5Ctextit%7Bratio%20from%20A%20to%20C%7D%7D%7B1%3A2%7D%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7BA%5Cunderline%7BB%7D%7D%7B%5Cunderline%7BB%7D%20C%7D%20%3D%20%5Ccfrac%7B1%7D%7B2%7D%5Cimplies%20%5Ccfrac%7BA%7D%7BC%7D%3D%5Ccfrac%7B1%7D%7B2%7D%5Cimplies%202A%3D1C%5Cimplies%202%28-9%2C-7%29%3D1%28x%2Cy%29%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20B%3D%5Cleft%28%5Cfrac%7B%5Ctextit%7Bsum%20of%20%22x%22%20values%7D%7D%7B%5Ctextit%7Bsum%20of%20ratios%7D%7D%5Cquad%20%2C%5Cquad%20%5Cfrac%7B%5Ctextit%7Bsum%20of%20%22y%22%20values%7D%7D%7B%5Ctextit%7Bsum%20of%20ratios%7D%7D%5Cright%29%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\bf B=\left(\cfrac{(2\cdot -9)+(1\cdot x)}{1+2}\quad ,\quad \cfrac{(2\cdot -7)+(1\cdot y)}{1+2}\right)~~=~~(-4,-6) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(2\cdot -9)+(1\cdot x)}{1+2}=-4\implies \cfrac{-18+x}{3}=-4 \\\\\\ -18+x=-12\implies \boxed{x=6} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(2\cdot -7)+(1\cdot y)}{1+2}=-6\implies \cfrac{-14+y}{3}=-6 \\\\\\ -14+y=-18\implies \boxed{y=-4}](https://tex.z-dn.net/?f=%5Cbf%20B%3D%5Cleft%28%5Ccfrac%7B%282%5Ccdot%20-9%29%2B%281%5Ccdot%20x%29%7D%7B1%2B2%7D%5Cquad%20%2C%5Cquad%20%5Ccfrac%7B%282%5Ccdot%20-7%29%2B%281%5Ccdot%20y%29%7D%7B1%2B2%7D%5Cright%29~~%3D~~%28-4%2C-6%29%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B%282%5Ccdot%20-9%29%2B%281%5Ccdot%20x%29%7D%7B1%2B2%7D%3D-4%5Cimplies%20%5Ccfrac%7B-18%2Bx%7D%7B3%7D%3D-4%20%5C%5C%5C%5C%5C%5C%20-18%2Bx%3D-12%5Cimplies%20%5Cboxed%7Bx%3D6%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B%282%5Ccdot%20-7%29%2B%281%5Ccdot%20y%29%7D%7B1%2B2%7D%3D-6%5Cimplies%20%5Ccfrac%7B-14%2By%7D%7B3%7D%3D-6%20%5C%5C%5C%5C%5C%5C%20-14%2By%3D-18%5Cimplies%20%5Cboxed%7By%3D-4%7D)
