The half angle formula is:
sin x/2 = +/- √ (( 1-cos x ) / 2 )
5π/12 = 5π/6 : 2
sin 5π/12 = +/- √(( 1 - cos ( 5π/6)) / 2 )
cos 5π/6 = cos 150° = -√3/2
≈ 0.966 ( this is sin 5π/12 )
For example,area = a, length = l, width = w
First we write two equations. The easier equation is the area equation, which we know to be
a = l x w
So that the first equation is :
<span>96 = l x w </span>
we make the second equation of the following statements :
<em>The length of a rectangle is 2 foot less than 3 times its width.</em>
<span>so it becomes :
l = 3w - 2
</span>
<span>To solve, we can use the substitution method.
</span>
![96 = l \times w\\96=(3w-2) \times w\\96=3w^{2}-2w\\3w^{2}-2w-96=0~~~~~~[now\ factor\ the\ equation]\\ (3w+16)(w-6)=0](https://tex.z-dn.net/?f=96%20%3D%20l%20%5Ctimes%20w%5C%5C96%3D%283w-2%29%20%5Ctimes%20w%5C%5C96%3D3w%5E%7B2%7D-2w%5C%5C3w%5E%7B2%7D-2w-96%3D0~~~~~~%5Bnow%5C%20factor%5C%20the%5C%20equation%5D%5C%5C%20%283w%2B16%29%28w-6%29%3D0)
<span><em>So if our width is 6, Now substitute the value of w = 6 into equation 2 </em></span>
So "w" = 6 and "l" = 16, and if we multiply them together, we get the correct area, 96. So our dimensions are 6 by 16.
Answer:
The answer to your question is a) C + J + S = 80
b) C = J + 5
c) S = 45 hours
Step-by-step explanation:
a) To represent the number of hours that they work together, just add the variables and equal them to 80.
Carlito + Juan + Sara = 80
C + J + S = 80 Equation l
b) Juan worked 5 hours more than Carlito
Juan = Carlito + 5
J = C + 5 Equation ll
c) Hours worked by Sara
S = 3J Equation lll
C = J - 5
Substitute equation ll and lll in equation l to find J
J - 5 + J + 3J = 80
5J = 80 - 5
5J = 75
J = 75/5
J = 15
-Find S
S = 3(15)
S = 45 hours
Answer:
(-6, 9) is the solution set for given system.
Step-by-step explanation:
Given that:
3x-y=-27 ----------- eq1
4x+2y=-6 --------- eq2
Solving by combining the equations:
Dividing eq2 by 2 we get:
2x + y = -3 ------- eq3
Now add eq1 and eq3, we get:
5x = -30 (y from both equations will be cancelled out)
Dividing both sides by 5:
x = -6
Now putting value of x back in eq3:
2(-6) + y = -3
-12 + y = -3
Adding 12 on both sides:
y = -3 + 12
y = 9
So the solution set for given system is (-6, 9)
i hope it will help you!
Answer:
Hello
Step-by-step explanation:
