Answer:
I think 512 feet in 16 seconds.
1. -1/5>-3/5 because we have like denominators we compare the inputs by the numerators.
2. 3/4 > 5/8 the least common denominator is: 8
Rewriting as equivalent fractions with the LCD:
3/4 = 6/8 5/8 = 5/8
Comparing the numerators of the equivalent fractions we have:
6/8 > 5/8
Rationalize the numerator:
![\dfrac{\sqrt{x+4}-2}x\cdot\dfrac{\sqrt{x+4}+2}{\sqrt{x+4}+2}=\dfrac{(\sqrt{x+4})^2-2^2}{x(\sqrt{x+4}+2)}=\dfrac x{x(\sqrt{x+4}+2)}=\dfrac1{\sqrt{x+4}+2}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%7Bx%2B4%7D-2%7Dx%5Ccdot%5Cdfrac%7B%5Csqrt%7Bx%2B4%7D%2B2%7D%7B%5Csqrt%7Bx%2B4%7D%2B2%7D%3D%5Cdfrac%7B%28%5Csqrt%7Bx%2B4%7D%29%5E2-2%5E2%7D%7Bx%28%5Csqrt%7Bx%2B4%7D%2B2%29%7D%3D%5Cdfrac%20x%7Bx%28%5Csqrt%7Bx%2B4%7D%2B2%29%7D%3D%5Cdfrac1%7B%5Csqrt%7Bx%2B4%7D%2B2%7D)
This is continuous at
, so we can evaluate the limit directly by substitution:
![\displaystyle\lim_{x\to0}\frac{\sqrt{x+4}-2}x=\lim_{x\to0}\frac1{\sqrt{x+4}+2}=\frac1{\sqrt4+2}=\frac14](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto0%7D%5Cfrac%7B%5Csqrt%7Bx%2B4%7D-2%7Dx%3D%5Clim_%7Bx%5Cto0%7D%5Cfrac1%7B%5Csqrt%7Bx%2B4%7D%2B2%7D%3D%5Cfrac1%7B%5Csqrt4%2B2%7D%3D%5Cfrac14)
The only values a cosine can have are from -1 to 1.
Step-by-step explanation:
sum of 5 times a number and -2, + 8n
becomes:
5n + (-2) + 8n, or
5n -2 +8n, or. 13n - 2