Answer:
142 degrees
Explanation:
First, you are going to estimate. You can quickly see that the angle is more than 90 degrees. The only option more than 90 degrees os 142 degrees.
18 because 6=22. 12=44. 18=66
The answer is 4.27 if it’s the blue painted ones
If triangle RST and triangle XYZ are similar, the statement that must be true is :
Angle R equals angle X
Triangle R S T
Triangle X Y Z
those three angles will be similar in this case
hope this helps
Answer:
and ![b=\frac{40}{13}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7B40%7D%7B13%7D)
Step-by-step explanation:
The equation of curve is
![2(x^2+y^2)^2=25(x^2-y^2)](https://tex.z-dn.net/?f=2%28x%5E2%2By%5E2%29%5E2%3D25%28x%5E2-y%5E2%29)
We need to find the equation of the tangent line to the curve at the point (-3, 1).
Differentiate with respect to x.
![2[2(x^2+y^2)\frac{d}{dx}(x^2+y^2)]=25(2x-2y\frac{dy}{dx})](https://tex.z-dn.net/?f=2%5B2%28x%5E2%2By%5E2%29%5Cfrac%7Bd%7D%7Bdx%7D%28x%5E2%2By%5E2%29%5D%3D25%282x-2y%5Cfrac%7Bdy%7D%7Bdx%7D%29)
![4(x^2+y^2)(2x+2y\frac{dy}{dx})=25(2x-2y\frac{dy}{dx})](https://tex.z-dn.net/?f=4%28x%5E2%2By%5E2%29%282x%2B2y%5Cfrac%7Bdy%7D%7Bdx%7D%29%3D25%282x-2y%5Cfrac%7Bdy%7D%7Bdx%7D%29)
The point of tangency is (-3,1). It means the slope of tangent is
.
Substitute x=-3 and y=1 in the above equation.
![4((-3)^2+(1)^2)(2(-3)+2(1)\frac{dy}{dx})=25(2(-3)-2(1)\frac{dy}{dx})](https://tex.z-dn.net/?f=4%28%28-3%29%5E2%2B%281%29%5E2%29%282%28-3%29%2B2%281%29%5Cfrac%7Bdy%7D%7Bdx%7D%29%3D25%282%28-3%29-2%281%29%5Cfrac%7Bdy%7D%7Bdx%7D%29)
![40(-6+2\frac{dy}{dx})=25(-6-2\frac{dy}{dx})](https://tex.z-dn.net/?f=40%28-6%2B2%5Cfrac%7Bdy%7D%7Bdx%7D%29%3D25%28-6-2%5Cfrac%7Bdy%7D%7Bdx%7D%29)
![-240+80\frac{dy}{dx})=-150-50\frac{dy}{dx}](https://tex.z-dn.net/?f=-240%2B80%5Cfrac%7Bdy%7D%7Bdx%7D%29%3D-150-50%5Cfrac%7Bdy%7D%7Bdx%7D)
![80\frac{dy}{dx}+50\frac{dy}{dx}=-150+240](https://tex.z-dn.net/?f=80%5Cfrac%7Bdy%7D%7Bdx%7D%2B50%5Cfrac%7Bdy%7D%7Bdx%7D%3D-150%2B240)
![130\frac{dy}{dx}=90](https://tex.z-dn.net/?f=130%5Cfrac%7Bdy%7D%7Bdx%7D%3D90)
Divide both sides by 130.
![\frac{dy}{dx}=\frac{9}{13}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7B9%7D%7B13%7D)
If a line passes through a points
with slope m, then the point slope form of the line is
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
The slope of tangent line is
and it passes through the point (-3,1). So, the equation of tangent is
![y-1=\frac{9}{13}(x-(-3))](https://tex.z-dn.net/?f=y-1%3D%5Cfrac%7B9%7D%7B13%7D%28x-%28-3%29%29)
![y-1=\frac{9}{13}(x)+\frac{27}{13}](https://tex.z-dn.net/?f=y-1%3D%5Cfrac%7B9%7D%7B13%7D%28x%29%2B%5Cfrac%7B27%7D%7B13%7D)
Add 1 on both sides.
![y=\frac{9}{13}(x)+\frac{27}{13}+1](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B9%7D%7B13%7D%28x%29%2B%5Cfrac%7B27%7D%7B13%7D%2B1)
![y=\frac{9}{13}(x)+\frac{40}{13}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B9%7D%7B13%7D%28x%29%2B%5Cfrac%7B40%7D%7B13%7D)
Therefore,
and
.