None of these are correct.
Answer:
![\infty](https://tex.z-dn.net/?f=%20%5Cinfty%20)
Step-by-step explanation:
If you meant infinity, that is the answer, I think you should elaborate on the question
Answer: x = 28
Step-by-step explanation:
x + 20=3x-36
20=2x-36
56=2x
56/2=28
So 28= x
Answer with Step-by-step explanation:
We are given that an equation of curve
![x^{\frac{2}{3}}+y^{\frac{2}{3}}=4](https://tex.z-dn.net/?f=x%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%2By%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%3D4)
We have to find the equation of tangent line to the given curve at point ![(-3\sqrt3,1)](https://tex.z-dn.net/?f=%28-3%5Csqrt3%2C1%29)
By using implicit differentiation, differentiate w.r.t x
Using formula :![\frac{dx^n}{dx}=nx^{n-1}](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%5En%7D%7Bdx%7D%3Dnx%5E%7Bn-1%7D)
![\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=-\frac{2}{3}x^{-\frac{1}{3}}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7Dy%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D%5Cfrac%7Bdy%7D%7Bdx%7D%3D-%5Cfrac%7B2%7D%7B3%7Dx%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D)
![\frac{dy}{dx}=\frac{-\frac{2}{3}x^{-\frac{1}{3}}}{\frac{2}{3}y^{-\frac{1}{3}}}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7B-%5Cfrac%7B2%7D%7B3%7Dx%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D%7D%7B%5Cfrac%7B2%7D%7B3%7Dy%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D%7D)
![\frac{dy}{dx}=-\frac{x^{-\frac{1}{3}}}{y^{-\frac{1}{3}}}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D-%5Cfrac%7Bx%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D%7D%7By%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D%7D)
Substitute the value x=![-3\sqrt3,y=1](https://tex.z-dn.net/?f=-3%5Csqrt3%2Cy%3D1)
Then, we get
![\frac{dy}{dx}=-\frac{(-3\sqrt3)^{-\frac{1}{3}}}{1}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D-%5Cfrac%7B%28-3%5Csqrt3%29%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D%7D%7B1%7D)
![\frac{dy}{dx}=-(-3^{\frac{3}{2}})^{-\frac{1}{3}}=-\frac{1}{-(3)^{\frac{3}{2}\times \frac{1}{3}}}=\frac{1}{\sqrt3}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D-%28-3%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D%3D-%5Cfrac%7B1%7D%7B-%283%29%5E%7B%5Cfrac%7B3%7D%7B2%7D%5Ctimes%20%5Cfrac%7B1%7D%7B3%7D%7D%7D%3D%5Cfrac%7B1%7D%7B%5Csqrt3%7D)
Slope of tangent=m=![\frac{1}{\sqrt3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Csqrt3%7D)
Equation of tangent line with slope m and passing through the point
is given by
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
Substitute the values then we get
The equation of tangent line is given by
![y-1=\frac{1}{\sqrt3}(x+3\sqrt3)](https://tex.z-dn.net/?f=y-1%3D%5Cfrac%7B1%7D%7B%5Csqrt3%7D%28x%2B3%5Csqrt3%29)
![y-1=\frac{x}{\sqrt3}+3](https://tex.z-dn.net/?f=y-1%3D%5Cfrac%7Bx%7D%7B%5Csqrt3%7D%2B3)
![y=\frac{x}{\sqrt3}+3+1](https://tex.z-dn.net/?f=y%3D%5Cfrac%7Bx%7D%7B%5Csqrt3%7D%2B3%2B1)
![y=\frac{x}{\sqrt3}+4](https://tex.z-dn.net/?f=y%3D%5Cfrac%7Bx%7D%7B%5Csqrt3%7D%2B4)
This is required equation of tangent line to the given curve at given point.
The correct answer, rounded to the nearest km², is 2694.
Explanation:
This can be represented using an exponential equation of the form
y = a(1+r)ˣ, where y is the total amount, a is the initial population, r is the rate of increase or decrease written as a decimal number, and x is the amount of time.
In our problem, a = 4200, r = -8.5% = -8.5/100 = -0.085, and x is 5:
y = 4200(1+-0.085)⁵ = 4200(0.915)⁵ = 2693.73 ≈ 2694.