![\bf \lim\limits_{x\to \infty}~\left( \cfrac{1}{8} \right)^x\implies \lim\limits_{x\to \infty}~\cfrac{1^x}{8^x}\\\\[-0.35em] ~\dotfill\\\\ \stackrel{x = 10}{\cfrac{1^{10}}{8^{10}}}\implies \cfrac{1}{8^{10}}~~,~~ \stackrel{x = 1000}{\cfrac{1^{1000}}{8^{1000}}}\implies \cfrac{1}{8^{1000}}~~,~~ \stackrel{x = 100000000}{\cfrac{1^{100000000}}{8^{100000000}}}\implies \cfrac{1}{8^{100000000}}~~,~~ ...](https://tex.z-dn.net/?f=%5Cbf%20%5Clim%5Climits_%7Bx%5Cto%20%5Cinfty%7D~%5Cleft%28%20%5Ccfrac%7B1%7D%7B8%7D%20%5Cright%29%5Ex%5Cimplies%20%5Clim%5Climits_%7Bx%5Cto%20%5Cinfty%7D~%5Ccfrac%7B1%5Ex%7D%7B8%5Ex%7D%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7Bx%20%3D%2010%7D%7B%5Ccfrac%7B1%5E%7B10%7D%7D%7B8%5E%7B10%7D%7D%7D%5Cimplies%20%5Ccfrac%7B1%7D%7B8%5E%7B10%7D%7D~~%2C~~%20%5Cstackrel%7Bx%20%3D%201000%7D%7B%5Ccfrac%7B1%5E%7B1000%7D%7D%7B8%5E%7B1000%7D%7D%7D%5Cimplies%20%5Ccfrac%7B1%7D%7B8%5E%7B1000%7D%7D~~%2C~~%20%5Cstackrel%7Bx%20%3D%20100000000%7D%7B%5Ccfrac%7B1%5E%7B100000000%7D%7D%7B8%5E%7B100000000%7D%7D%7D%5Cimplies%20%5Ccfrac%7B1%7D%7B8%5E%7B100000000%7D%7D~~%2C~~%20...)
now, if we look at the values as "x" races fast towards ∞, we can as you see above, use the values of 10, 1000, 100000000 and so on, as the value above oddly enough remains at 1, it could have been smaller but it's constantly 1 in this case, the value at the bottom is ever becoming a larger and larger denominator.
let's recall that the larger the denominator, the smaller the fraction, so the expression is ever going towards a tiny and tinier and really tinier fraction, a fraction that is ever approaching 0.
Answer:
(x+9)^2 + (y-4)^2 = 4
Step-by-step explanation:
The equation for a circle is (x-h)^2 + (y-k)^2 = r^2
Answer:
Given that the height is 26 feet, the height of the stories of the building is 26-6=20 feet. therefore, the height of each story of the building is 20÷2=10
First, I would distribute the 2 out to the (x+4).
2x+8.
Next, use the foil method to multiply together 2x+8 and (x+3).
2x^2 +14x+24.
Do the same process for the other side.
3(x+2)= 3x+6
(3x+6)(x-1)= 3x^2+3x-6
Set the remaining products of each side of the equation equal to each other.
2x^2 +14x+24=3x^2+3x-6.
Now you must cancel out one side to make the equation equal to zero. Do this by doing the inverse operation on one side of the equation (each value with their like term). I am going to subtract the left side values from the right:
This means:
3x^2 minus 2x^2 equals 1x^2 (or just x^2).
3x minus 14x equals -11x
-6 minus 24 equals -30
The equation should now look like this:
0=x^2-11x-30
Reverse the order to get zero on the right side:
x^2-11x-30=0
Hope this helps! Sorry if I made any careless mistakes (^^;)
