Answer:
18 inches
Step-by-step explanation:
Given: The heights of both cylinders are 48 inches and 32 inches. Diameter of the larger cylinder is 12 inches
To find: diameter of the larger cylinder
Solution:
Height of the larger cylinder (H) = 48 inches
Height of the smaller cylinder (h) = 32 inches
Diameter of the smaller cylinder (d) = 12 inches
Radius of the smaller cylinder (r) = d/2 =12/ 2= 6 inches
As two cylinders are similar, their heights and radii are proportional.
![\frac{r}{h}=\frac{R}{H}\\\frac{6}{32}=\frac{R}{48}\\R=\frac{6}{32}\times 48=9\,\,inches](https://tex.z-dn.net/?f=%5Cfrac%7Br%7D%7Bh%7D%3D%5Cfrac%7BR%7D%7BH%7D%5C%5C%5Cfrac%7B6%7D%7B32%7D%3D%5Cfrac%7BR%7D%7B48%7D%5C%5CR%3D%5Cfrac%7B6%7D%7B32%7D%5Ctimes%2048%3D9%5C%2C%5C%2Cinches)
Diameter of the larger cylinder = 2R = 2(9) = 18 inches
Answer: a
n
=
10
n
−
111
Step-by-step explanation:
Use the formula a
n
=
a
1
+d
(
n
−
1
) to identify the arithmetic sequence.
a
n
=
10
n
−
111
Answer:
45.45%
Step-by-step explanation:
freshman and sophomores over total students
(110+65)/(110+65+95+50)
175/385
45.45%
Answer:
1 and 3; 2 and 4
Step-by-step explanation:
Supplementary angles add up to 180 degrees, which is a straight line.
we can see that angles 2 and 3 make the / line, as do 1 and 4
1 and 2 make up the \ line, while, as mentioned above, 2 and 3 make /
4 and 1 is the same as 1 and 4 so they still create / and angles 3 and 4 make the \
Explanation
The model has the form
![y=ae^{-kt}](https://tex.z-dn.net/?f=y%3Dae%5E%7B-kt%7D)
Where a=initial amount
y= final amount
K= growth rate constant
t= time
When 140 kg of substance is left after 7 hours, the formula can be remodeled to be.
![\begin{gathered} 140=400e^{-7k} \\ e^{-7k}=\frac{140}{400} \\ e^{-7k}=\frac{7}{20} \\ \ln (e^{-7k})=\ln (\frac{7}{20}) \\ -7k=\ln (\frac{7}{20}) \\ k=\frac{\ln(\frac{7}{20})}{-7} \\ \therefore k=\frac{\ln (\frac{20}{7})}{7} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20140%3D400e%5E%7B-7k%7D%20%5C%5C%20e%5E%7B-7k%7D%3D%5Cfrac%7B140%7D%7B400%7D%20%5C%5C%20e%5E%7B-7k%7D%3D%5Cfrac%7B7%7D%7B20%7D%20%5C%5C%20%5Cln%20%28e%5E%7B-7k%7D%29%3D%5Cln%20%28%5Cfrac%7B7%7D%7B20%7D%29%20%5C%5C%20-7k%3D%5Cln%20%28%5Cfrac%7B7%7D%7B20%7D%29%20%5C%5C%20k%3D%5Cfrac%7B%5Cln%28%5Cfrac%7B7%7D%7B20%7D%29%7D%7B-7%7D%20%5C%5C%20%5Ctherefore%20k%3D%5Cfrac%7B%5Cln%20%28%5Cfrac%7B20%7D%7B7%7D%29%7D%7B7%7D%20%5Cend%7Bgathered%7D)
Therefore, the first solution is
![y=400e^{-\ln (\frac{20}{7})\frac{t}{7}}](https://tex.z-dn.net/?f=y%3D400e%5E%7B-%5Cln%20%28%5Cfrac%7B20%7D%7B7%7D%29%5Cfrac%7Bt%7D%7B7%7D%7D)
For part b we have 16 hours.
![\begin{gathered} y=400e^{-\ln (\frac{20}{7})\frac{t}{7}}=400e^{-\ln (\frac{20}{7})\frac{16}{7}} \\ y=36.302\approx36\operatorname{kg}\text{ (To the nearest whole number)} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3D400e%5E%7B-%5Cln%20%28%5Cfrac%7B20%7D%7B7%7D%29%5Cfrac%7Bt%7D%7B7%7D%7D%3D400e%5E%7B-%5Cln%20%28%5Cfrac%7B20%7D%7B7%7D%29%5Cfrac%7B16%7D%7B7%7D%7D%20%5C%5C%20y%3D36.302%5Capprox36%5Coperatorname%7Bkg%7D%5Ctext%7B%20%28To%20the%20nearest%20whole%20number%29%7D%20%5Cend%7Bgathered%7D)
Thus, the answer is 36kg