Answer:
yes the first one is best answer because its a lower # to pay over time Step-by-step explanation:
Angle b° is an inscribed angle, then its measurement is the half of the arc:
m angle b° = arc/2
m angle b° = 60°/2
m angle b°=30°
b=30
Answer: Fourth option: 30
<u>Answer- </u>
The directional derivative of f(x,y) at (0,6) in the direction θ = 2π/3 is, 7.73
<u>Solution-</u>
The unit vector in the direction of the given angle is
![\hat{u}= < \cos \frac{2\pi }{3} , \sin \frac{2\pi }{3}> \ = \](https://tex.z-dn.net/?f=%5Chat%7Bu%7D%3D%20%3C%20%5Ccos%20%5Cfrac%7B2%5Cpi%20%7D%7B3%7D%20%2C%20%5Csin%20%5Cfrac%7B2%5Cpi%20%7D%7B3%7D%3E%20%5C%20%3D%20%5C%20%3C%5Cfrac%7B-1%7D%7B2%7D%20%2C%20%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%20%3E)
Given that,
![f(x,y)=2ye^{-x}](https://tex.z-dn.net/?f=f%28x%2Cy%29%3D2ye%5E%7B-x%7D)
Gradient of f(x,y)
![\triangledown f(x,y) = < -2ye^{-x} ,2e^{-x} >](https://tex.z-dn.net/?f=%5Ctriangledown%20f%28x%2Cy%29%20%3D%20%3C%20-2ye%5E%7B-x%7D%20%2C2e%5E%7B-x%7D%20%3E)
Gradient of f(x,y) at (0,6)
= <(-2)(6)(1) , (2)(1)> = <-12 , 2>
The directional derivative of f(x,y) at (0,6) is
![\triangledown f(0,6)\cdot \hat{u} \ = \ \cdot = (-12)(\frac{-1}{2} )+(2)(\frac{\sqrt{3}}{2})= 6+\sqrt{3} = 7.73](https://tex.z-dn.net/?f=%5Ctriangledown%20f%280%2C6%29%5Ccdot%20%5Chat%7Bu%7D%20%5C%20%3D%20%5C%20%3C-12%20%2C%202%3E%5Ccdot%3C%5Cfrac%7B-1%7D%7B2%7D%2C%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%20%20%3E%20%3D%20%28-12%29%28%5Cfrac%7B-1%7D%7B2%7D%20%29%2B%282%29%28%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%29%3D%206%2B%5Csqrt%7B3%7D%20%3D%207.73)
1. 50% of 60mins is 30mins
2. 10% of 60 mins is 6mins
3.75% of 60 mins is 45mins