The tangent vector to r(<em>t</em>) at any <em>t</em> in the domain is
![\mathbf T(t)=\dfrac{\mathrm d\mathbf r(t)}{\mathrm dt}=2\cos t\,\mathbf i-7\sin t\,\mathbf j](https://tex.z-dn.net/?f=%5Cmathbf%20T%28t%29%3D%5Cdfrac%7B%5Cmathrm%20d%5Cmathbf%20r%28t%29%7D%7B%5Cmathrm%20dt%7D%3D2%5Ccos%20t%5C%2C%5Cmathbf%20i-7%5Csin%20t%5C%2C%5Cmathbf%20j)
At <em>t</em> = π/6, the tanget vector is
![\mathbf T\left(\dfrac\pi6\right)=\sqrt3\,\mathbf i-\dfrac72\,\mathbf j](https://tex.z-dn.net/?f=%5Cmathbf%20T%5Cleft%28%5Cdfrac%5Cpi6%5Cright%29%3D%5Csqrt3%5C%2C%5Cmathbf%20i-%5Cdfrac72%5C%2C%5Cmathbf%20j)
To get the unit tangent, normalize this vector by dividing it by its magnitude:
![\left\|\mathbf T\left(\dfrac\pi6\right)\right\|=\sqrt{(\sqrt3)^2+\left(-\dfrac72\right)^2}=\dfrac{\sqrt{61}}2](https://tex.z-dn.net/?f=%5Cleft%5C%7C%5Cmathbf%20T%5Cleft%28%5Cdfrac%5Cpi6%5Cright%29%5Cright%5C%7C%3D%5Csqrt%7B%28%5Csqrt3%29%5E2%2B%5Cleft%28-%5Cdfrac72%5Cright%29%5E2%7D%3D%5Cdfrac%7B%5Csqrt%7B61%7D%7D2)
So the unit tangent at the given point is
![\dfrac{\mathbf T\left(\frac\pi6\right)}{\left\|\mathbf T\left(\frac\pi6\right)\right\|}=2\sqrt{\dfrac3{61}}\,\mathbf i-\dfrac7{\sqrt{61}}\,\mathbf j](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathbf%20T%5Cleft%28%5Cfrac%5Cpi6%5Cright%29%7D%7B%5Cleft%5C%7C%5Cmathbf%20T%5Cleft%28%5Cfrac%5Cpi6%5Cright%29%5Cright%5C%7C%7D%3D2%5Csqrt%7B%5Cdfrac3%7B61%7D%7D%5C%2C%5Cmathbf%20i-%5Cdfrac7%7B%5Csqrt%7B61%7D%7D%5C%2C%5Cmathbf%20j)
Slope is 9 or 9/1 and the y-intercept is -9 or (0,-9)
Answer:
tell me how to do it tell me and i will try
Answer:
psst whats wrong??
Step-by-step explanation:
Answer:
he gets alot of money and is very good at what he does
so his income per year is around
551,800$ a year your welcome
but if we are doing and average
i need to devide by 2
so his average a year might just be
275,900$ a year
vote brainliest hope this helps
Step-by-step explanation: