Answer:
Similar but not congruent
Step-by-step explanation:
They look to be the same shape, but they aren't the same exact size so they cant be congruent. To be congruent they would have to be the same size and shape, but they are only the same shape, different sizes.
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.
Answer:
7
Step-by-step explanation:
they r the same angle bc they are on parallel lines and being crossed with a line at one angle
hope this helped
plz mark brainliest i wanna rank up ;P
Answer:
D. none of these
Step-by-step explanation:
apples: 6 pounds
oranges: 24 pounds
bananas: 3 pounds
total: 33 pounds
answer:
D. none of these