Answer:
![Sin \angle A =0.80](https://tex.z-dn.net/?f=Sin%20%5Cangle%20A%20%3D0.80)
![Cos \angle A=0.60](https://tex.z-dn.net/?f=Cos%20%5Cangle%20A%3D0.60)
![Sin \angle B =0.60](https://tex.z-dn.net/?f=Sin%20%5Cangle%20B%20%3D0.60)
![Cos \angle B=0.80](https://tex.z-dn.net/?f=Cos%20%5Cangle%20B%3D0.80)
Step-by-step explanation:
Given
I will answer this question using the attached triangle
Solving (a): Sine and Cosine A
In trigonometry:
and
![Cos \theta =\frac{Adjacent}{Hypotenuse}](https://tex.z-dn.net/?f=Cos%20%5Ctheta%20%3D%5Cfrac%7BAdjacent%7D%7BHypotenuse%7D)
So:
![Sin \angle A =\frac{BC}{BA}](https://tex.z-dn.net/?f=Sin%20%5Cangle%20A%20%3D%5Cfrac%7BBC%7D%7BBA%7D)
Substitute values for BC and BA
![Sin \angle A =\frac{8cm}{10cm}](https://tex.z-dn.net/?f=Sin%20%5Cangle%20A%20%3D%5Cfrac%7B8cm%7D%7B10cm%7D)
![Sin \angle A =\frac{8}{10}](https://tex.z-dn.net/?f=Sin%20%5Cangle%20A%20%3D%5Cfrac%7B8%7D%7B10%7D)
![Sin \angle A =0.80](https://tex.z-dn.net/?f=Sin%20%5Cangle%20A%20%3D0.80)
![Cos \angle A=\frac{AC}{BA}](https://tex.z-dn.net/?f=Cos%20%5Cangle%20A%3D%5Cfrac%7BAC%7D%7BBA%7D)
Substitute values for AC and BA
![Cos \angle A=\frac{6cm}{10cm}](https://tex.z-dn.net/?f=Cos%20%5Cangle%20A%3D%5Cfrac%7B6cm%7D%7B10cm%7D)
![Cos \angle A=\frac{6}{10}](https://tex.z-dn.net/?f=Cos%20%5Cangle%20A%3D%5Cfrac%7B6%7D%7B10%7D)
![Cos \angle A=0.60](https://tex.z-dn.net/?f=Cos%20%5Cangle%20A%3D0.60)
Solving (b): Sine and Cosine B
In trigonometry:
and
![Cos \theta =\frac{Adjacent}{Hypotenuse}](https://tex.z-dn.net/?f=Cos%20%5Ctheta%20%3D%5Cfrac%7BAdjacent%7D%7BHypotenuse%7D)
So:
![Sin \angle B =\frac{AC}{BA}](https://tex.z-dn.net/?f=Sin%20%5Cangle%20B%20%3D%5Cfrac%7BAC%7D%7BBA%7D)
Substitute values for AC and BA
![Sin \angle B =\frac{6cm}{10cm}](https://tex.z-dn.net/?f=Sin%20%5Cangle%20B%20%3D%5Cfrac%7B6cm%7D%7B10cm%7D)
![Sin \angle B =\frac{6}{10}](https://tex.z-dn.net/?f=Sin%20%5Cangle%20B%20%3D%5Cfrac%7B6%7D%7B10%7D)
![Sin \angle B =0.60](https://tex.z-dn.net/?f=Sin%20%5Cangle%20B%20%3D0.60)
![Cos \angle B=\frac{BC}{BA}](https://tex.z-dn.net/?f=Cos%20%5Cangle%20B%3D%5Cfrac%7BBC%7D%7BBA%7D)
Substitute values for BC and BA
![Cos \angle B=\frac{8cm}{10cm}](https://tex.z-dn.net/?f=Cos%20%5Cangle%20B%3D%5Cfrac%7B8cm%7D%7B10cm%7D)
![Cos \angle B=\frac{8}{10}](https://tex.z-dn.net/?f=Cos%20%5Cangle%20B%3D%5Cfrac%7B8%7D%7B10%7D)
![Cos \angle B=0.80](https://tex.z-dn.net/?f=Cos%20%5Cangle%20B%3D0.80)
Using a calculator:
![A = 53^{\circ}](https://tex.z-dn.net/?f=A%20%3D%2053%5E%7B%5Ccirc%7D)
So:
![Sin(53^{\circ}) =0.7986](https://tex.z-dn.net/?f=Sin%2853%5E%7B%5Ccirc%7D%29%20%3D0.7986)
-- approximated
![Cos(53^{\circ}) = 0.6018](https://tex.z-dn.net/?f=Cos%2853%5E%7B%5Ccirc%7D%29%20%3D%200.6018)
-- approximated
![B = 37^{\circ}](https://tex.z-dn.net/?f=B%20%3D%2037%5E%7B%5Ccirc%7D)
So:
![Sin(37^{\circ}) = 0.6018](https://tex.z-dn.net/?f=Sin%2837%5E%7B%5Ccirc%7D%29%20%3D%200.6018)
--- approximated
![Cos(37^{\circ}) = 0.7986](https://tex.z-dn.net/?f=Cos%2837%5E%7B%5Ccirc%7D%29%20%3D%200.7986)
--- approximated
Answer:
Option 3 is correct that is ![(6+s)(s^2-6s+36)](https://tex.z-dn.net/?f=%286%2Bs%29%28s%5E2-6s%2B36%29)
Step-by-step explanation:
We have general formula for sum of cube which is
![a^3+b^3=(a+b)(a^2+b^2-ab)](https://tex.z-dn.net/?f=a%5E3%2Bb%5E3%3D%28a%2Bb%29%28a%5E2%2Bb%5E2-ab%29)
Here, we have a=s and b=6
on substituting the values in the formula we will get
![6^3+s^3=(6+s)(s^2+6^2-6s)](https://tex.z-dn.net/?f=6%5E3%2Bs%5E3%3D%286%2Bs%29%28s%5E2%2B6%5E2-6s%29)
After simplification we will get
![6^3+s^3=(6+s)(s^2+36-6s)](https://tex.z-dn.net/?f=6%5E3%2Bs%5E3%3D%286%2Bs%29%28s%5E2%2B36-6s%29)
After rearranging the terms we will get
which exactly matches option 3 in the given options.
Therefore, option 3 is correct that is ![(6+s)(s^2-6s+36)](https://tex.z-dn.net/?f=%286%2Bs%29%28s%5E2-6s%2B36%29)
Answer:
Slope=14.000/2.000=7.000
x-intercept = 300/-7 = -42.85714
y-intercept = 300/1 = 300.00000
Step-by-step explanation:
Answer:
c=|x-7|
Step-by-step explanation:
The answers you are looking for are:
A.) 199580
B.) 114002
C.) 48042
D.) 5828
E.) 18510
Hope that helps!!
Have a wonderful day!!