Where is the graph if any?
Answer:
See explanation
Step-by-step explanation:
We have to prove the identity
![tan(\frac{\Theta }{2})=\frac{sin\Theta}{1+cos\Theta }](https://tex.z-dn.net/?f=tan%28%5Cfrac%7B%5CTheta%20%7D%7B2%7D%29%3D%5Cfrac%7Bsin%5CTheta%7D%7B1%2Bcos%5CTheta%20%7D)
We will take right hand side of the identity
![\frac{sin\Theta}{1+cos\Theta}=\frac{2sin(\frac{\Theta }{2})cos(\frac{\Theta }{2})}{1+[2cos^{2}(\frac{\Theta }{2})-1]}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%5CTheta%7D%7B1%2Bcos%5CTheta%7D%3D%5Cfrac%7B2sin%28%5Cfrac%7B%5CTheta%20%7D%7B2%7D%29cos%28%5Cfrac%7B%5CTheta%20%7D%7B2%7D%29%7D%7B1%2B%5B2cos%5E%7B2%7D%28%5Cfrac%7B%5CTheta%20%7D%7B2%7D%29-1%5D%7D)
![=\frac{2sin(\frac{\Theta }{2})cos(\frac{\Theta }{2})}{2cos^{2}(\frac{\Theta }{2})}=\frac{sin(\frac{\Theta }{2})}{cos(\frac{\Theta }{2})}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B2sin%28%5Cfrac%7B%5CTheta%20%7D%7B2%7D%29cos%28%5Cfrac%7B%5CTheta%20%7D%7B2%7D%29%7D%7B2cos%5E%7B2%7D%28%5Cfrac%7B%5CTheta%20%7D%7B2%7D%29%7D%3D%5Cfrac%7Bsin%28%5Cfrac%7B%5CTheta%20%7D%7B2%7D%29%7D%7Bcos%28%5Cfrac%7B%5CTheta%20%7D%7B2%7D%29%7D)
[ Tan θ will be positive since θ lies in 1st quadrant ]
Answer:
4,050 ft^3
Step-by-step explanation:
Separate the figure into a cube and a square pyramid.
Volume of the cube (a^3):
15 x 15 x 15 = 3,375
3,375 ft^3
Volume of the square pyramid (lwh/3):
15 x 15 x 9/3 = 675
675 ft^3
Add the volumes of both figures:
675 ft^3 + 3,375 ft^3 = 4,050
The volume of the whole figure is 4,050 cubic feet.
Hope this helps!
70+68= 138
138 is the answer because by the triangle sum theorem says all the inside angles of a triangle equal 180 degrees and a straight line is 180 degrees so to find x you just must add up the other two sides of the triangle
Answer:
x = 21°
y = 29°
Step-by-step explanation:
a) Solving for x
Note that:
(3x - 3)° and 60° are Alternate interior angles, and alternate interior angles are equal to each other, hence:
3x - 3 = 60° (Alternate interior angles)
Add 3 to both sides
3x - 3 +3 = 60 + 3
3x = 63°
x = 63°/3
x = 21°
b) Solving for y
Notes that:
(3x - 3)° and (4y + 4)° are Consecutive interior angles and the sum consecutive interior angles is 180°
3x - 3 + 4y + 4 = 180°
3x + 4y - 3 + 4 = 180°
3x + 4y + 1 = 180°
Note that x = 21
Hence
3(21) + 4y + 1 = 180°
63 + 1 + 4y = 180°
64 + 4y = 180°
Subtract 64 from both sides
64 - 64 + 4y = 180° - 64
4y = 116°
y = 116/4
y => 29°