Answer:
m∠CAF is 28°
Step-by-step explanation:
The given parameters are;
EG = 3, EB = 8, A_F = 7, m∠EBG = 23°, ∠EGF 32°, and m∠CAE = 51°
From the diagram, we have;
m∠EBG = m∠EAD ; 
Given
Therefore, m∠EAD = 23°
m∠CAE = m∠CAF + m∠EAD Angle addition postulate
Therefore, we have;
51° = m∠CAF + 23°
m∠CAF = 51° - 23°
m∠CAF = 28°
Answer:
2 real solutions
Step-by-step explanation:
y = -x^2 + 3x + 5
First find the the discriminant:
using b² - 4(a)(b)
(3)²- 4(-1)(5)
=9+20
=29
since the discriminant is more than 0, there are 2 real solutions
5*8+2
When a letter is next to a number u multiply
5*8+2=42
<span>Acceleration of a passenger is centripetal acceleration, since the Ferris wheel is assumed at uniform speed:
a = omega^2*r
omega and r in terms of given data:
omega = 2*Pi/T
r = d/2
Thus:
a = 2*Pi^2*d/T^2
What forces cause this acceleration for the passenger, at either top or bottom?
At top (acceleration is downward):
Weight (m*g): downward
Normal force (Ntop): upward
Thus Newton's 2nd law reads:
m*g - Ntop = m*a
At top (acceleration is upward):
Weight (m*g): downward
Normal force (Nbottom): upward
Thus Newton's 2nd law reads:
Nbottom - m*g = m*a
Solve for normal forces in both cases. Normal force is apparent weight, the weight that the passenger thinks is her weight when measuring by any method in the gondola reference frame:
Ntop = m*(g - a)
Nbottom = m*(g + a)
Substitute a:
Ntop = m*(g - 2*Pi^2*d/T^2)
Nbottom = m*(g + 2*Pi^2*d/T^2)
We are interested in the ratio of weight (gondola reference frame weight to weight when on the ground):
Ntop/(m*g) = m*(g - 2*Pi^2*d/T^2)/(m*g)
Nbottom/(m*g) = m*(g + 2*Pi^2*d/T^2)/(m*g)
Simplify:
Ntop/(m*g) = 1 - 2*Pi^2*d/(g*T^2)
Nbottom/(m*g) = 1 + 2*Pi^2*d/(g*T^2)
Data:
d:=22 m; T:=12.5 sec; g:=9.8 N/kg;
Results:
Ntop/(m*g) = 71.64%...she feels "light"
Nbottom/(m*g) = 128.4%...she feels "heavy"</span>
Answer:
127 degrees
Step-by-step explanation:
540 degrees is what the interior of a pentagon should add up to. So you do 540-156-72-98-87=127. The measure of the final interior angle is 127 degrees.
