Answer:
The definite integral expressing the total quantity of oil, 'V', which leaks out of the tanker in the first hour is given as follows;
![V = \int\limits^{60}_0 {A \cdot e^{(-k \cdot t)}} \, dt](https://tex.z-dn.net/?f=V%20%3D%20%5Cint%5Climits%5E%7B60%7D_0%20%7BA%20%5Ccdot%20e%5E%7B%28-k%20%5Ccdot%20t%29%7D%7D%20%5C%2C%20dt)
Step-by-step explanation:
From the question, we have;
The rate at which oil leaks out of the tanker, r = f(t)
The unit of the oil leak = Liters per minute
The unit of t = Minutes
![If \ f(t) = A \cdot e^{(-k \cdot t )}](https://tex.z-dn.net/?f=If%20%5C%20f%28t%29%20%3D%20A%20%5Ccdot%20e%5E%7B%28-k%20%5Ccdot%20t%20%29%7D)
Therefore, we have;
The definite integral expressing the total quantity, 'V', of oil which leaks out of the tanker in the first hour is given as follows;
![V = \int\limits^{60}_0 {A \cdot e^{(-k \cdot t)}} \, dt](https://tex.z-dn.net/?f=V%20%3D%20%5Cint%5Climits%5E%7B60%7D_0%20%7BA%20%5Ccdot%20e%5E%7B%28-k%20%5Ccdot%20t%29%7D%7D%20%5C%2C%20dt)
Therefore, we have;
![\int\limits^{60}_0 {A \cdot e^{(-k \cdot t)}} \, dt = \dfrac{A \cdot e ^{60 \cdot k} - A}{k \cdot e ^{60 \cdot k} }](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B60%7D_0%20%7BA%20%5Ccdot%20e%5E%7B%28-k%20%5Ccdot%20t%29%7D%7D%20%5C%2C%20dt%20%3D%20%5Cdfrac%7BA%20%5Ccdot%20e%20%5E%7B60%20%5Ccdot%20k%7D%20-%20A%7D%7Bk%20%5Ccdot%20e%20%5E%7B60%20%5Ccdot%20k%7D%20%7D)
Answer:
D. Min (3, -4)
Step-by-step explanation:
This curve is a parabola, the graph of a quadratic function. It has a kind of u-ish, v-ish shape. Right there at the bottom, where the curve appears to be making a u-turn, is the vertex. That point is at (3,-4).
Also, it is a low point of the curve, which makes it a minimum of this upward opening parabola. Sometimes this curve can be flipped upside down, in which case it would have maximum.
But this one has a minimum at (3,-4)
C = 180 - 53
c = 127
d = 540 - (127 + 114 + 92 + 119 )
d = 540 - 452
d = 88
e = 180 - 88
e = 92
Answer: wouldn't be <u>18 m</u> because half is 9 m.
HOPE THIS HELPS :D
Answer:
263.9 cm^3 to nearest tenth.
Step-by-step explanation:
V = 1/3 π r^2 h
= 1/3 π 6^2 7
= 12 * 7 π
= 84π
= 263.8938