Answer:
x≥2.56
Step-by-step explanation:
first we can write the inequality
2+9x≥25
we can now solve this with algebra
9x≥23
x≥2.56
Answer: 34.2
For everyone 1 kilometer=.621371 so if you times that by 55 you get 34.1754 which rounds to 34.2
Think of PEMDAS, or Please Excuse My Dear Aunt Sally. Which is Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction in that order.
Answer:
Step-by-step explanation: hope this help :)
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.