Answer: 5.22
Step-by-step explanation:
Given
![\angle A=103^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20A%3D103%5E%7B%5Ccirc%7D)
Sine law is ![\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\\](https://tex.z-dn.net/?f=%5Cdfrac%7Ba%7D%7B%5Csin%20A%7D%3D%5Cdfrac%7Bb%7D%7B%5Csin%20B%7D%3D%5Cdfrac%7Bc%7D%7B%5Csin%20C%7D%5C%5C)
Here, a=8, c=5
Putting values
![\Rightarrow \dfrac{8}{\sin 103}=\dfrac{5}{\sin C}\\\\\Rightarrow \sin C=\dfrac{5}{8}\sin 103^{\circ}=0.6089\\\Rightarrow C=37.51^{\circ}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7B8%7D%7B%5Csin%20103%7D%3D%5Cdfrac%7B5%7D%7B%5Csin%20C%7D%5C%5C%5C%5C%5CRightarrow%20%5Csin%20C%3D%5Cdfrac%7B5%7D%7B8%7D%5Csin%20103%5E%7B%5Ccirc%7D%3D0.6089%5C%5C%5CRightarrow%20C%3D37.51%5E%7B%5Ccirc%7D)
![\Rightarrow \angle B=180^{\circ} -103^{\circ}-37.51^{\circ}\\\Rightarrow \angle B=39.49^{\circ}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cangle%20B%3D180%5E%7B%5Ccirc%7D%20-103%5E%7B%5Ccirc%7D-37.51%5E%7B%5Ccirc%7D%5C%5C%5CRightarrow%20%5Cangle%20B%3D39.49%5E%7B%5Ccirc%7D)
If b=m, then
![\Rightarrow \dfrac{8}{\sin 103^{\circ}}=\dfrac{m}{\sin 39.49^{\circ}}\\\\\Rightarrow m=\dfrac{\sin 39.49^{\circ}}{\sin 103^{\circ}}\times 8=5.22](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7B8%7D%7B%5Csin%20103%5E%7B%5Ccirc%7D%7D%3D%5Cdfrac%7Bm%7D%7B%5Csin%2039.49%5E%7B%5Ccirc%7D%7D%5C%5C%5C%5C%5CRightarrow%20m%3D%5Cdfrac%7B%5Csin%2039.49%5E%7B%5Ccirc%7D%7D%7B%5Csin%20103%5E%7B%5Ccirc%7D%7D%5Ctimes%208%3D5.22)
Answer:
72.89 degrees
Step-by-step explanation:
![tangent = \frac{opposite}{adjacent} \\ tangent = \frac{13}{4} \\ tangent = 72.89 \: or \: 72.9 \: degrees](https://tex.z-dn.net/?f=tangent%20%3D%20%20%5Cfrac%7Bopposite%7D%7Badjacent%7D%20%20%5C%5C%20tangent%20%3D%20%20%20%5Cfrac%7B13%7D%7B4%7D%20%20%5C%5C%20tangent%20%3D%2072.89%20%5C%3A%20or%20%5C%3A%2072.9%20%5C%3A%20degrees)
3x8 1x4
—— + ——
4x8 8x4
24 4
—- + —-
32 32
28
5 —-
32
Answer:
x f(x)
–3 –12
–1 –4
4 16
Step-by-step explanation:
Let us find the each function by evaluating them one by one
1.
x f(x)
–3 –12 = -3 x 4
–1 –4 = -1 x 4
4 16 = 4 x 4
By observing the data we can see that
f(x) = 4x
2.
x f(x)
–2 6 = -2 x -3
–1 3 = -1 x -3
1 –3= 1 x -3
f(x) = -3x
3.
x f(x)
1 0.25 = 1/4
8 2 = 8/4
16 4 = 16/4
f(x)= x/4
4.
x f(x)
–9 3 = -9/-3
–3 1 = -3/-3
21 –7 = 21/-3
f(x) = x/-3
Hence comparing all the four function with our given function f(x)=3x , we see that f(x) =4x has a greater rate of change that f(x)=3x