The ratio between the lengths of 2 rectangles is the same between their perimeters
![l_1\colon l_2=P_1\colon P_2](https://tex.z-dn.net/?f=l_1%5Ccolon%20l_2%3DP_1%5Ccolon%20P_2)
Since the ratio between the length of rectangle A and the length of rectangle B is 7: 3, then
The ratio between the perimeter of rectangle A to the perimeter of rectangle B is 7: 3 too
![\begin{gathered} l_A\colon l_B=7\colon3 \\ P_A\colon P_B=7\colon3 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20l_A%5Ccolon%20l_B%3D7%5Ccolon3%20%5C%5C%20P_A%5Ccolon%20P_B%3D7%5Ccolon3%20%5Cend%7Bgathered%7D)
Since the perimeter of rectangle A is 540, then
![540\colon P_B=7\colon3](https://tex.z-dn.net/?f=540%5Ccolon%20P_B%3D7%5Ccolon3)
We will write them as a fraction
![\frac{540}{P_B}=\frac{7}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B540%7D%7BP_B%7D%3D%5Cfrac%7B7%7D%7B3%7D)
By using the cross multiplication
![\begin{gathered} P_B\times7=540\times3 \\ 7P_B=1620 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20P_B%5Ctimes7%3D540%5Ctimes3%20%5C%5C%207P_B%3D1620%20%5Cend%7Bgathered%7D)
Divide both sides by 7
![\begin{gathered} \frac{7P_B}{7}=\frac{1620}{7} \\ P_B=231.4285714 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B7P_B%7D%7B7%7D%3D%5Cfrac%7B1620%7D%7B7%7D%20%5C%5C%20P_B%3D231.4285714%20%5Cend%7Bgathered%7D)
Round it to the nearest tenth
![P_B=231.4\text{ inches}](https://tex.z-dn.net/?f=P_B%3D231.4%5Ctext%7B%20inches%7D)
The perimeter of the smaller rectangle B is 231.4 inches
Answer:
hypotenuse
Step-by-step explanation:
Remember that when using sin and cos functions, the hypotenuse is always included as the denominator of the equation EXCEPT when you're solving with tan, which is opposite/adjacent.
Given:
The growth of a sample of bacteria can be modeled by the function
![b(t)=1001.06t](https://tex.z-dn.net/?f=b%28t%29%3D1001.06t)
where, b is the number of bacteria and t is time in hours.
To find:
The number of total bacteria after 3 hours.
Solution:
We have,
![b(t)=1001.06t](https://tex.z-dn.net/?f=b%28t%29%3D1001.06t)
where, b is the number of bacteria and t is time in hours.
Substituting t=3, we get the number of total bacteria after 3 hours.
![b(3)=1001.06(3)](https://tex.z-dn.net/?f=b%283%29%3D1001.06%283%29)
![b(3)=3003.18](https://tex.z-dn.net/?f=b%283%29%3D3003.18)
Number of bacteria cannot be decimal value. So, approximate the value to the nearest whole number.
![b(3)\approx 3003](https://tex.z-dn.net/?f=b%283%29%5Capprox%203003)
Therefore, the number of total bacteria after 3 hours is about 3003.