1/2 = 2/4;
Compare 2/4 with 3/4;
Because 2 < 3, we have 2/4<3/4;
Finally, 1/2<3/4;
The correct answer is D.
Answer:
Angle 1 - 51
Angle 2 - 39
Angle 3 - 90
Angle 4 - 51
Angle 5 - 17
Angle 6 - 129
Step-by-step explanation:
Angle 1 = 180 - 90 - 39 = 51
Angle 2 = 90 - Angle 2 (51) = 39
Angle 3 = 90
Angle 4 = 180 - Angle 2 (39) - Angle 3 (90) = 51
Angle 5 = 180- 90 - 34 -39 = 17
Angle 6 = 180 - Angle 4 (51) = 129
We know that
2π/3 radians-------> convert to degrees-----> 2*180/3---> 120°
120°=90°+30°
Part a) Find <span>sin(2π/3)
</span>sin(2π/3)=sin (90°+30°)
we know that
sin (A+B)=sin A*cos B+cos A*sin B
so
sin (90°+30°)=sin 90*cos 30+cos 90*sin 30
sin 90=1
cos 30=√3/2
cos 90=0
sin 30=1/2
sin (90°+30°)=1*√3/2+0*1/2-----> √3/2
the answer part a) is
sin(2π/3)=√3/2
Part b) Find cos (2π/3)
cos (2π/3)=cos (90°+30°)
we know that
cos (A+B)=cos A*cos B-sin A*sin B
so
cos (90°+30°)=cos 90*cos 30-sin 90*sin 30
sin 90=1
cos 30=√3/2
cos 90=0
sin 30=1/2
cos (90°+30°)=0*√3/2-1*1/2----> -1/2
the answer part b) is
cos (2π/3)=-1/2
The maximum radius of each ball is 3.33 cm.
<h3>What is a Cylinder?</h3>
A cylinder is a three-dimensional figure which is made of two parallel circular bases separated at a certain distance by a curved surface of the same radius as that of the bases.
A 20 cm nail perfectly fits the cylinder.
So the height of the cylinder = 20cm.
A sphere is a three-dimensional geometrical figure analogous to a circle. All the points of the sphere are at the same distance from the center.
If 3 spheres have to be fitted inside the cylinder,
The sum of the diameter of the spheres will be equal to the height of the cylinder.
The spherical balls are identical and so will have the same diameter
Let the maximum diameter of the sphere that can fit in the cylinder is d cm
Then,
d + d + d = 20
3d = 20
d = 20/3 = 6.67 cm
r = 3.33 cm
The maximum radius that the spheres can have to fit in the cylinder is 3.33 cm.
To know more about Cylinder
brainly.com/question/16134180
#SPJ1
Answer:
a = 3.9
Step-by-step explanation:
Isolate the varible by dividing each side by factors that don't contain the variable.
