Step-by-step explanation:
step 1. f(0) = 0/(0^2 + 1) = 0/1 = 0
step 2. -f(x) = -x/(x^2 + 1)
step 3. f(9) = 9/(9^2 + 1) = 9/82.
There are no sharp objects around,same with bleach
Answer:
31 degrees
Step-by-step explanation:
Difference in temperature from 2:00 pm to 2:00 am = 27 - (-4) = 27 + 4 = 31 degrees
Given:
![$\frac{\left(\frac{(4 r)^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{(3 t)^{2}}\right)}](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Cleft%28%5Cfrac%7B%284%20r%29%5E%7B3%7D%7D%7B15%20t%5E%7B4%7D%7D%5Cright%29%7D%7B%5Cleft%28%5Cfrac%7B16%20r%7D%7B%283%20t%29%5E%7B2%7D%7D%5Cright%29%7D)
To find:
The simplified fraction.
Solution:
Step 1: Simplify the numerator
![$\frac{(4 r)^{3}}{15 t^{4}}=\frac{4^3 r^{3}}{15 t^{4}}=\frac{64 r^{3}}{15 t^{4}}](https://tex.z-dn.net/?f=%24%5Cfrac%7B%284%20r%29%5E%7B3%7D%7D%7B15%20t%5E%7B4%7D%7D%3D%5Cfrac%7B4%5E3%20r%5E%7B3%7D%7D%7B15%20t%5E%7B4%7D%7D%3D%5Cfrac%7B64%20r%5E%7B3%7D%7D%7B15%20t%5E%7B4%7D%7D)
Step 2: Simplify the denominator
![$\frac{16 r}{(3 t)^{2}}=\frac{16 r}{3^2 t^{2}}= \frac{16 r}{9 t^{2}}](https://tex.z-dn.net/?f=%24%5Cfrac%7B16%20r%7D%7B%283%20t%29%5E%7B2%7D%7D%3D%5Cfrac%7B16%20r%7D%7B3%5E2%20t%5E%7B2%7D%7D%3D%20%5Cfrac%7B16%20r%7D%7B9%20t%5E%7B2%7D%7D)
Step 3: Using step 1 and step 2
![$\frac{\left(\frac{(4 r)^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{(3 t)^{2}}\right)}=\frac{\left(\frac{64 r^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{9 t^{2}} \right)}](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Cleft%28%5Cfrac%7B%284%20r%29%5E%7B3%7D%7D%7B15%20t%5E%7B4%7D%7D%5Cright%29%7D%7B%5Cleft%28%5Cfrac%7B16%20r%7D%7B%283%20t%29%5E%7B2%7D%7D%5Cright%29%7D%3D%5Cfrac%7B%5Cleft%28%5Cfrac%7B64%20r%5E%7B3%7D%7D%7B15%20t%5E%7B4%7D%7D%5Cright%29%7D%7B%5Cleft%28%5Cfrac%7B16%20r%7D%7B9%20t%5E%7B2%7D%7D%20%5Cright%29%7D)
Step 4: Using fraction rule:
![$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a \cdot d}{b \cdot c}](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Cfrac%7Ba%7D%7Bb%7D%7D%7B%5Cfrac%7Bc%7D%7Bd%7D%7D%3D%5Cfrac%7Ba%20%5Ccdot%20d%7D%7Bb%20%5Ccdot%20c%7D)
![$\frac{\left(\frac{64 r^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{9 t^{2}}\right)}=\frac{64r^3 \cdot 9t^2}{16 r \cdot 15 t^4}](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Cleft%28%5Cfrac%7B64%20r%5E%7B3%7D%7D%7B15%20t%5E%7B4%7D%7D%5Cright%29%7D%7B%5Cleft%28%5Cfrac%7B16%20r%7D%7B9%20t%5E%7B2%7D%7D%5Cright%29%7D%3D%5Cfrac%7B64r%5E3%20%5Ccdot%209t%5E2%7D%7B16%20r%20%5Ccdot%2015%20t%5E4%7D)
Cancel the common factor r and t², we get
![$=\frac{64 r^{2} \cdot 9 }{16 \cdot 15 t^2 }](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B64%20r%5E%7B2%7D%20%5Ccdot%209%20%7D%7B16%20%20%5Ccdot%2015%20t%5E2%20%7D)
Cancel the common factors 16 and 3 on both numerator and denominator.
![$=\frac{4 r^{2} \cdot 3 }{ 5 t^2 }](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B4%20r%5E%7B2%7D%20%5Ccdot%203%20%7D%7B%20%205%20t%5E2%20%7D)
![$=\frac{12 r^{2} }{ 5 t^2 }](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B12%20r%5E%7B2%7D%20%20%7D%7B%20%205%20t%5E2%20%7D)
![$\frac{\left(\frac{(4 r)^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{(3 t)^{2}}\right)}=\frac{12 r^{2} }{ 5 t^2 }](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Cleft%28%5Cfrac%7B%284%20r%29%5E%7B3%7D%7D%7B15%20t%5E%7B4%7D%7D%5Cright%29%7D%7B%5Cleft%28%5Cfrac%7B16%20r%7D%7B%283%20t%29%5E%7B2%7D%7D%5Cright%29%7D%3D%5Cfrac%7B12%20r%5E%7B2%7D%20%20%7D%7B%20%205%20t%5E2%20%7D)
The simplified fraction is
.
Answer:38
Step-by-step explanation:
you put 3 in front of 8 and you get 38