Answer:
Termaine has to spend $8.00 on each of the four people.
Step-by-step explanation:
32÷4=8
Answer:
see explanation
Step-by-step explanation:
The statements tells us that w is inversely proportional to v and the equation relating them is
v =
← k is the constant of proportion
To find k use the condition v = 9, w = 5, that is
9 =
( multiply both sides by 5 )
45 = k
v =
← equation of proportion
When w = 4 , then
v =
= 11.25
Mars is the correct answer
Recall the Pythagorean identity,
![\sin^2(\theta) + \cos^2(\theta) = 1](https://tex.z-dn.net/?f=%5Csin%5E2%28%5Ctheta%29%20%2B%20%5Ccos%5E2%28%5Ctheta%29%20%3D%201)
Since
belongs to Q3, we know both
and
are negative. Then
![\cos(\theta) = -\sqrt{1 - \sin^2(\theta)} = -\dfrac7{25}](https://tex.z-dn.net/?f=%5Ccos%28%5Ctheta%29%20%3D%20-%5Csqrt%7B1%20-%20%5Csin%5E2%28%5Ctheta%29%7D%20%3D%20-%5Cdfrac7%7B25%7D)
Recall the half-angle identities for sine and cosine,
![\sin^2\left(\dfrac\theta2\right) = \dfrac{1 - \cos(\theta)}2](https://tex.z-dn.net/?f=%5Csin%5E2%5Cleft%28%5Cdfrac%5Ctheta2%5Cright%29%20%3D%20%5Cdfrac%7B1%20-%20%5Ccos%28%5Ctheta%29%7D2)
![\cos^2\left(\dfrac\theta2\right) = \dfrac{1 + \cos(\theta)}2](https://tex.z-dn.net/?f=%5Ccos%5E2%5Cleft%28%5Cdfrac%5Ctheta2%5Cright%29%20%3D%20%5Cdfrac%7B1%20%2B%20%5Ccos%28%5Ctheta%29%7D2)
Then by definition of tangent,
![\tan^2\left(\dfrac\theta2\right) = \dfrac{\sin^2\left(\frac\theta2\right)}{\cos^2\left(\frac\theta2\right)} = \dfrac{1 - \cos(\theta)}{1 + \cos(\theta)}](https://tex.z-dn.net/?f=%5Ctan%5E2%5Cleft%28%5Cdfrac%5Ctheta2%5Cright%29%20%3D%20%5Cdfrac%7B%5Csin%5E2%5Cleft%28%5Cfrac%5Ctheta2%5Cright%29%7D%7B%5Ccos%5E2%5Cleft%28%5Cfrac%5Ctheta2%5Cright%29%7D%20%3D%20%5Cdfrac%7B1%20-%20%5Ccos%28%5Ctheta%29%7D%7B1%20%2B%20%5Ccos%28%5Ctheta%29%7D)
belonging to Q3 means
, or
, so that the half-angle belongs to Q2. Then
is positive and
is negative, so
is negative.
It follows that
![\tan\left(\dfrac\theta2\right) = -\sqrt{\dfrac{1 - \cos(\theta)}{1 + \cos(\theta)}} = \boxed{-\dfrac43}](https://tex.z-dn.net/?f=%5Ctan%5Cleft%28%5Cdfrac%5Ctheta2%5Cright%29%20%3D%20-%5Csqrt%7B%5Cdfrac%7B1%20-%20%5Ccos%28%5Ctheta%29%7D%7B1%20%2B%20%5Ccos%28%5Ctheta%29%7D%7D%20%3D%20%5Cboxed%7B-%5Cdfrac43%7D)