![\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.
8. The percentage of salt in each mixture is 0.35%.
To find out the latter part of the problem, we can use algebra:
14 (grams of salt) = 0.35m (0.35% of the mixture)
14 ÷ 0.35 = 0.35m ÷ 0.35 (we want to find just m, so we have to divide it by 0.35)
40 = m. The scientist made 40 g of mixture!
9. We just divide 32.5 pounds by 0.25 ( a quarter).
32.5 ÷ 0.25 = 130 kids!
10. Her original distance is 0.5 miles. But! She walked back 0.25 (quarter) mile so now this adds a quarter of a mile of distance from her house to her school.
0.5 × 3 = 1.5 + 0.25 = 1.75 miles from her house to her school.
Answer:
c
Step-by-step explanation:
Answer:
y = (3/4)x - 9
Step-by-step explanation:
The slope-intercept form of the equation of a straight line is y = mx + b.
Here we know x, y and m, but must find b.
Substituting 8 for x, -3 for y and 3/4 for m in the equation above results in:
-3 = (3/4)(8) + b, or (after multiplying all three terms by 4 to clear fractions):
-3 = 6 + b
Then b = -9, and the desired equation is y = (3/4)x - 9
Answer:
5x+3y+5/2(5 over 2)
Step-by-step explanation:
Divide 10 by 2
divide 6 by 2
divide 5 by 2 and you stay at 5/2
