I don’t think you can calculate the arc without the radius. All I know is that the angle is 110 degree
Answer:
4
Step-by-step explanation:
2N - 3 = 5
2N = 5 +3 = 8
N = 8/2 = 4
we are given
The scale is

the distance from Happy Hill Park to Rainbow Valley Park is 4 1/2 inches
we can change it into rational form
and we get

so, we can multiply both sides by 9

now, we can simplify it

so, the actual distance between the two parks is 27 miles........Answer
tis a little of plain differentiation.
we know the radius of the cone is decreasing at 10 mtr/mins, or namely dr/dt = -10, decreasing, meaning is negative.
we know the volume is decreasing at a rate of 1346 mtr/mins or namely dV/dt = -1346, also negative.
so, when h = 9 and V = 307, what is dh/dt in essence.
we'll be needing the "r" value at that instant, so let's get it

now let's get the derivative of the volume of the cone
![V=\cfrac{1}{3}\pi r^2 h\implies \cfrac{dV}{dt}=\cfrac{\pi }{3}\stackrel{product~rule}{ \left[ \underset{chain~rule}{2r\cdot \cfrac{dr}{dt}}\cdot h+r^2\cdot \cfrac{dh}{dt} \right]} \\\\\\ -1346=\cfrac{\pi }{3}\left[2\sqrt{\cfrac{307}{3\pi }}(-10)(9)~~+ ~~ \cfrac{307}{3\pi } \cdot \cfrac{dh}{dt}\right]](https://tex.z-dn.net/?f=V%3D%5Ccfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2%20h%5Cimplies%20%5Ccfrac%7BdV%7D%7Bdt%7D%3D%5Ccfrac%7B%5Cpi%20%7D%7B3%7D%5Cstackrel%7Bproduct~rule%7D%7B%20%5Cleft%5B%20%5Cunderset%7Bchain~rule%7D%7B2r%5Ccdot%20%5Ccfrac%7Bdr%7D%7Bdt%7D%7D%5Ccdot%20h%2Br%5E2%5Ccdot%20%5Ccfrac%7Bdh%7D%7Bdt%7D%20%5Cright%5D%7D%20%5C%5C%5C%5C%5C%5C%20-1346%3D%5Ccfrac%7B%5Cpi%20%7D%7B3%7D%5Cleft%5B2%5Csqrt%7B%5Ccfrac%7B307%7D%7B3%5Cpi%20%7D%7D%28-10%29%289%29~~%2B%20~~%20%5Ccfrac%7B307%7D%7B3%5Cpi%20%7D%20%5Ccdot%20%5Ccfrac%7Bdh%7D%7Bdt%7D%5Cright%5D)
![-\cfrac{4038}{\pi }=-\cfrac{180\sqrt{307}}{\sqrt{3\pi }}+\cfrac{307}{3\pi } \cdot \cfrac{dh}{dt}\implies \left[ -\cfrac{4038}{\pi }+\cfrac{180\sqrt{307}}{\sqrt{3\pi }} \right]\cfrac{3\pi }{307}=\cfrac{dh}{dt} \\\\\\ -\cfrac{12114}{307}+\cfrac{180\sqrt{3\pi }}{\sqrt{307}}=\cfrac{dh}{dt}\implies -7.920939735970634 \approx \cfrac{dh}{dt}](https://tex.z-dn.net/?f=-%5Ccfrac%7B4038%7D%7B%5Cpi%20%7D%3D-%5Ccfrac%7B180%5Csqrt%7B307%7D%7D%7B%5Csqrt%7B3%5Cpi%20%7D%7D%2B%5Ccfrac%7B307%7D%7B3%5Cpi%20%7D%20%5Ccdot%20%5Ccfrac%7Bdh%7D%7Bdt%7D%5Cimplies%20%5Cleft%5B%20-%5Ccfrac%7B4038%7D%7B%5Cpi%20%7D%2B%5Ccfrac%7B180%5Csqrt%7B307%7D%7D%7B%5Csqrt%7B3%5Cpi%20%7D%7D%20%5Cright%5D%5Ccfrac%7B3%5Cpi%20%7D%7B307%7D%3D%5Ccfrac%7Bdh%7D%7Bdt%7D%20%5C%5C%5C%5C%5C%5C%20-%5Ccfrac%7B12114%7D%7B307%7D%2B%5Ccfrac%7B180%5Csqrt%7B3%5Cpi%20%7D%7D%7B%5Csqrt%7B307%7D%7D%3D%5Ccfrac%7Bdh%7D%7Bdt%7D%5Cimplies%20-7.920939735970634%20%5Capprox%20%5Ccfrac%7Bdh%7D%7Bdt%7D)
Answer:
The solution is ![\frac{1}{10} * tan^{-1}[\frac{e^{2x}}{5} ] + C](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B10%7D%20%2A%20tan%5E%7B-1%7D%5B%5Cfrac%7Be%5E%7B2x%7D%7D%7B5%7D%20%5D%20%2B%20%20C)
Step-by-step explanation:
From the question
The function given is 
The indefinite integral is mathematically represented as

Now let 
=> 
=> 
So

![= \frac{1}{2} \frac{tan^{-1} [\frac{u}{5} ]}{5} + C](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cfrac%7Btan%5E%7B-1%7D%20%5B%5Cfrac%7Bu%7D%7B5%7D%20%5D%7D%7B5%7D%20%20%2B%20%20C)
Now substituting for u
![\frac{1}{10} * tan^{-1}[\frac{e^{2x}}{5} ] + C](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B10%7D%20%2A%20tan%5E%7B-1%7D%5B%5Cfrac%7Be%5E%7B2x%7D%7D%7B5%7D%20%5D%20%2B%20%20C)