Answer:
Step-by-step explanation:
The model fo the shell is given by the following equation of equilibrium:
This first-order differential equation has separable variables, which are cleared herein:
The solution of this integral is:
![t = -\frac{m}{2b}\cdot \left[\tan^{-1} \left(\frac{v}{\sqrt{\frac{m\cdot g}{b} } }\right) - \tan^{-1} \left(\frac{600}{\sqrt{\frac{m\cdot g}{b} } }\right)\right]](https://tex.z-dn.net/?f=t%20%3D%20-%5Cfrac%7Bm%7D%7B2b%7D%5Ccdot%20%5Cleft%5B%5Ctan%5E%7B-1%7D%20%5Cleft%28%5Cfrac%7Bv%7D%7B%5Csqrt%7B%5Cfrac%7Bm%5Ccdot%20g%7D%7Bb%7D%20%7D%20%7D%5Cright%29%20-%20%5Ctan%5E%7B-1%7D%20%5Cleft%28%5Cfrac%7B600%7D%7B%5Csqrt%7B%5Cfrac%7Bm%5Ccdot%20g%7D%7Bb%7D%20%7D%20%7D%5Cright%29%5Cright%5D)
![\frac{v}{\sqrt{\frac{m\cdot g}{b} } }=\tan \left[-\frac{2\cdot b\cdot t}{m} + \tan^{-1}\left(\frac{600}{\sqrt{\frac{m\cdot g}{b} } } \right)\right]](https://tex.z-dn.net/?f=%5Cfrac%7Bv%7D%7B%5Csqrt%7B%5Cfrac%7Bm%5Ccdot%20g%7D%7Bb%7D%20%7D%20%7D%3D%5Ctan%20%5Cleft%5B-%5Cfrac%7B2%5Ccdot%20b%5Ccdot%20t%7D%7Bm%7D%20%2B%20%5Ctan%5E%7B-1%7D%5Cleft%28%5Cfrac%7B600%7D%7B%5Csqrt%7B%5Cfrac%7Bm%5Ccdot%20g%7D%7Bb%7D%20%7D%20%7D%20%20%5Cright%29%5Cright%5D)
![v = \sqrt{\frac{m\cdot g}{b} } \left [\frac{\tan \left(-\frac{2\cdot b \cdot t}{m} \right)+ \left(\frac{600}{\sqrt{\frac{m\cdot g}{b} } } \right)}{1 - \left(\frac{600}{\sqrt{\frac{m\cdot g}{b} } } \right)\cdot \tan \left(-\frac{2\cdot b \cdot t}{m} \right) }\right]](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B%5Cfrac%7Bm%5Ccdot%20g%7D%7Bb%7D%20%7D%20%5Cleft%20%5B%5Cfrac%7B%5Ctan%20%5Cleft%28-%5Cfrac%7B2%5Ccdot%20b%20%5Ccdot%20t%7D%7Bm%7D%20%20%5Cright%29%2B%20%5Cleft%28%5Cfrac%7B600%7D%7B%5Csqrt%7B%5Cfrac%7Bm%5Ccdot%20g%7D%7Bb%7D%20%7D%20%7D%20%20%5Cright%29%7D%7B1%20-%20%5Cleft%28%5Cfrac%7B600%7D%7B%5Csqrt%7B%5Cfrac%7Bm%5Ccdot%20g%7D%7Bb%7D%20%7D%20%7D%20%20%5Cright%29%5Ccdot%20%5Ctan%20%5Cleft%28-%5Cfrac%7B2%5Ccdot%20b%20%5Ccdot%20t%7D%7Bm%7D%20%20%5Cright%29%20%7D%5Cright%5D)
Answer:
Step-by-step explanation:
-5/3,-0.5,-1/3,0.5,1.25
Answer:
Step-by-step explanation:
In finding the COMMON DIFFERENCE, subtract the 2nd term and the first term.
a1 = -4
a2 = -2
Let "d" representing the COMMON DIFFERENCE.
d = -2 -(-4)
d = -2 + 4
d = 2
ANSWER:
THE COMMON DIFFERENCE OF THIS SEQUENCE IS 2
For the given function, the domain is D : { x ≥ 7} and the range is R: { y ≥ 9}
<h3>
How to get the domain and range?</h3>
Here we have a square root, remember that the argument of the square root must be equal or larger than zero, so the domain is such that:
x - 7 ≥ 0.
Solving for x we get:
x ≥ 0 + 7
Then the domain is:
x ≥ 7
To get the range, we evaluate in the minimum of the domain:
f(7) = √(7 - 7) + 9 = 9
Then the range is the set of all values larger than 9, because the function is increasing.
So the range is R: y ≥ 9.
If you want to learn more about domain and range:
brainly.com/question/10197594
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