C=2πr
We have 3/4 of circumference
(3π/2)*2π=3/4.
and it is equal 5π/2.
(3/4)*C=(3/4)*2πr
5π/2 = 6πr/4
5/2=6r/4
r=(5/2)*(4/6)=(5*4)/(2*6)=5/3
r=5/3
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:
The three consecutive integers are 5,6,7
Step-by-step explanation:
Let the three consecutive integers be represented as x,x+1,x+2
As per the requirement, largest integer is 3 less than twice the smallest.
=> x+ 2 = 2x -3
=> 2x -x = 2+3
=> x= 5
So the three integers are 5,6,7
Verification:
Largest integer = 7
Smallest integer = 5
2 * smallest integer - 3 = 2* 5 - 3 = 7
Largest integer is also 7.
So the required condition in the question is satisfied by these three integers.
2000 x 1.03^5 = $2318.55
i think this question is about compound interest so my answer should be correct i hope it helps
