Answer:
27
Step-by-step explanation:
![(f\circ g)(x)=f(g(x))\\\\(f\circ g)(2) = f(g(2)) = f(2\cdot 2+3) = f(7)\\\\=4\cdot 7-1=\boxed{27}](https://tex.z-dn.net/?f=%28f%5Ccirc%20g%29%28x%29%3Df%28g%28x%29%29%5C%5C%5C%5C%28f%5Ccirc%20g%29%282%29%20%3D%20f%28g%282%29%29%20%3D%20f%282%5Ccdot%202%2B3%29%20%3D%20f%287%29%5C%5C%5C%5C%3D4%5Ccdot%207-1%3D%5Cboxed%7B27%7D)
Answer:
43 and 56/12
Step-by-step explanation:
Answer:
Approximately 1705 liters of oil leaked out during the first hour.
Step-by-step explanation:
We are given the following in the question:
The rate of oil leak is given by:
![r(t) = 75 e^{-0.04}](https://tex.z-dn.net/?f=r%28t%29%20%3D%2075%20e%5E%7B-0.04%7D)
This function gives the rate of leakage in liters per minute.
We have to find the amount of water leak during the first hour.
It can be calculated as:
![r(t) = 75 e^{-0.04t}\\\text{Integrating both sides}\\\\\displaystyle\int^{60}_0 = \int^{60}_0 75 e^{-0.04t}dt\\\\=\bigg[\dfrac{75 e^{-0.04t}}{-0.04}\bigg]^{60}_0\\\\=-1875\big[e^{-0.04(60)}-e^{0}\big]\\=-1875(0.0907-1)\\=1704.90\\\approx 1705](https://tex.z-dn.net/?f=r%28t%29%20%3D%2075%20e%5E%7B-0.04t%7D%5C%5C%5Ctext%7BIntegrating%20both%20sides%7D%5C%5C%5C%5C%5Cdisplaystyle%5Cint%5E%7B60%7D_0%20%3D%20%5Cint%5E%7B60%7D_0%2075%20e%5E%7B-0.04t%7Ddt%5C%5C%5C%5C%3D%5Cbigg%5B%5Cdfrac%7B75%20e%5E%7B-0.04t%7D%7D%7B-0.04%7D%5Cbigg%5D%5E%7B60%7D_0%5C%5C%5C%5C%3D-1875%5Cbig%5Be%5E%7B-0.04%2860%29%7D-e%5E%7B0%7D%5Cbig%5D%5C%5C%3D-1875%280.0907-1%29%5C%5C%3D1704.90%5C%5C%5Capprox%201705)
Thus, approximately 1705 liters of oil leaked out during the first hour.
Answer:
267 students
Step-by-step explanation:
Number of students in a team (t) is proportional to number of honor roll students (n)
Mathematically, t = kn (k is constant
When t = 12, n = 8
k = t/n = 12/8 = 1.5
When t = 400
n = t/k = 400/1.5 = 267 (to the nearest whole number)
Answer:\ a.The wire is part of the electric circuit. The electric current will not flow if it breaks
Step-by-step explanation:
Hope this helps!