![\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.
Step-by-step explanation:
When we compare 2 system of equations (of the form y = mx + c), we take note of the following things:
- If the values of m and c in both equations are the same, they have infinitely many solutions
- If only the value of m is the same, they have no solutions
- If neither is the same, they have 1 solution
Bearing this in mind, we have the following answers:
y = -6x - 2 and y = -6x - 2
=> Infinitely many solutions
y = 0.5x + 5 and y = 0.5x + 1
=> No solutions
y = 0.25x + 2 and y = 5x - 4
=> 1 solution
y = 2x + 3 and y = 4x - 1
=> 1 solution
y = 2x + 5 and y = 2x + 5
=> Infinitely many solutions
y = -x - 3 and y = -x + 3
=> No solutions
Answer:
$1200
Step-by-step explanation:
$1200
Step-by-step explanation:
78 = 6.5%
This means that if you divide 78 by 6.5, you get the equivalent of 1% of the price:
78 ÷ 6.5 = 12
So 1% = 12
Now simply multiply this by 100 to get the full answer:
12 x 100 = 1200
So the camera cost $1200!
Answer:
Dr. Kora will pay an interest of $6,000
Step-by-step explanation:
Simple interest = P × R × T
Where:
P = Principal = $8000
R = Rate = 7.5% = 0.075
T = Time = 10 years
∴ Simple interest = 8000 × 0.075 × 10 = $6,000
Therefore Dr. Kora will pay an interest of $6,000
Wouldnt it be:
9 9
--- = -------- = 9
3-2 1
