98 divided by 2 equals 49
55 divided by 5 equals 11
Answer:
Step-by-step explanation:
(a)
Consider the following:

Use sine rule,
![\frac{b}{a}=\frac{\sinB}{\sin A} \\\\=\frac{\sin{\frac{\pi}{3}} }{\sin{\frac{\pi}{4}}}\\\\=\frac{[\frac{\sqrt{3}}{2}]}{\frac{1}{\sqrt{2}}}\\\\=\frac{\sqrt{2}}{2}\times \frac{\sqrt{2}}{1}=\sqrt{\frac{3}{2}}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7Ba%7D%3D%5Cfrac%7B%5CsinB%7D%7B%5Csin%20A%7D%0A%5C%5C%5C%5C%3D%5Cfrac%7B%5Csin%7B%5Cfrac%7B%5Cpi%7D%7B3%7D%7D%0A%7D%7B%5Csin%7B%5Cfrac%7B%5Cpi%7D%7B4%7D%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B%5B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%5D%7D%7B%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5Ctimes%20%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B1%7D%3D%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D)
Again consider,
![\frac{b}{a}=\frac{\sin{B}}{\sin{A}} \\\\\sin{B}=\frac{b}{a}\times \sin{A}\\\\\sin{B}=\sqrt{\frac{3}{2}}\sin {A}\\\\B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{A}]](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7Ba%7D%3D%5Cfrac%7B%5Csin%7BB%7D%7D%7B%5Csin%7BA%7D%7D%0A%5C%5C%5C%5C%5Csin%7BB%7D%3D%5Cfrac%7Bb%7D%7Ba%7D%5Ctimes%20%5Csin%7BA%7D%5C%5C%5C%5C%5Csin%7BB%7D%3D%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Csin%20%7BA%7D%5C%5C%5C%5CB%3D%5Csin%5E%7B-1%7D%5B%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Csin%7BA%7D%5D)
Thus, the angle B is function of A is, ![B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{A}]](https://tex.z-dn.net/?f=B%3D%5Csin%5E%7B-1%7D%5B%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Csin%7BA%7D%5D)
Now find 
Differentiate implicitly the function
with respect to A to get,

b)
When
, the value of
is,

c)
In general, the linear approximation at x= a is,

Here the function ![f(A)=B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{A}]](https://tex.z-dn.net/?f=f%28A%29%3DB%3D%5Csin%5E%7B-1%7D%5B%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Csin%7BA%7D%5D)
At 
![f(\frac{\pi}{4})=B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{\frac{\pi}{4}}]\\\\=\sin^{-1}[\sqrt{\frac{3}{2}}.\frac{1}{\sqrt{2}}]\\\\\=\sin^{-1}(\frac{\sqrt{2}}{2})\\\\=\frac{\pi}{3}](https://tex.z-dn.net/?f=f%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%3DB%3D%5Csin%5E%7B-1%7D%5B%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Csin%7B%5Cfrac%7B%5Cpi%7D%7B4%7D%7D%5D%5C%5C%5C%5C%3D%5Csin%5E%7B-1%7D%5B%5Csqrt%7B%5Cfrac%7B3%7D%7B2%7D%7D.%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%5D%5C%5C%5C%5C%5C%3D%5Csin%5E%7B-1%7D%28%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%29%5C%5C%5C%5C%3D%5Cfrac%7B%5Cpi%7D%7B3%7D)
And,
from part b
Therefore, the linear approximation at
is,
![f(x)=f'(A).(x-A)+f(A)\\\\=f'(\frac{\pi}{4}).(x-\frac{\pi}{4})+f(\frac{\pi}{4})\\\\=\sqrt{3}.[x-\frac{\pi}{4}]+\frac{\pi}{3}](https://tex.z-dn.net/?f=f%28x%29%3Df%27%28A%29.%28x-A%29%2Bf%28A%29%5C%5C%5C%5C%3Df%27%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29.%28x-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%2Bf%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5C%5C%5C%5C%3D%5Csqrt%7B3%7D.%5Bx-%5Cfrac%7B%5Cpi%7D%7B4%7D%5D%2B%5Cfrac%7B%5Cpi%7D%7B3%7D)
d)
Use part (c), when
, B is approximately,
![B=f(46°)=\sqrt{3}[46°-\frac{\pi}{4}]+\frac{\pi}{3}\\\\=\sqrt{3}(1°)+\frac{\pi}{3}\\\\=61.732°](https://tex.z-dn.net/?f=B%3Df%2846%C2%B0%29%3D%5Csqrt%7B3%7D%5B46%C2%B0-%5Cfrac%7B%5Cpi%7D%7B4%7D%5D%2B%5Cfrac%7B%5Cpi%7D%7B3%7D%5C%5C%5C%5C%3D%5Csqrt%7B3%7D%281%C2%B0%29%2B%5Cfrac%7B%5Cpi%7D%7B3%7D%5C%5C%5C%5C%3D61.732%C2%B0)
A. 75 degrees because the angle creates by the car and the opposite 75 degree are vertical angles meaning that their congruent
B. 75 degrees because the 4the street and the 3rd streets are both Patel meaning that the angle of the car and the 75 degree angle on northeast angle of the fourth street are corresponding angels
C. 105 degrees because the 180 degrees which is the angle of a straight line subtracted from the 75 degree gives the answer of 105 degrees
The required value if r = 32 and d = 2 is -3
Given the expression

Substituting the given variables
r = 32
d = 2
The expression becomes

Hence the required value is -3
Learn more here: brainly.com/question/17499155
Answer:
3)76°
Step-by-step explanation:
- y=76°{vertically opposite angle r equal}
hope it helps.