Answer:
Step-by-step explanation:
tan x/2=-√3/3
sec²x/2-tan²x/2=1
sec²x/2-3/9=1
sec² x/2=1+1/3=4/3
cos² x/2=3/4
2cos² x/2=3/2
1+cos x=3/2
cos x=3/2-1=1/2=cos π/3,cos (2π-π/3)
x=π/3,5π/3
or
cos x=(1-tan²x/2)/(1+tan²x/2)=(1-1/3)(1+1/3)=(2/3)/(4/3)=1/2=cos π/3,cos (2π-π/3)
or x=π/3,5π/3
x=π/3
x/2=π/6
tan x/2=tan π/6=√3/3
so x=π/3 is an extraneous value.
x=5π/3 is the solution.
or
tan x/2=-√3/3=-1/√3=(-1/2)/(√3/2) [by dividing numerator and denominator by 2]
=-tan π/6=tan (π-π/6),tan (2π-π/6)
x/2=5π/6,11π/6
x=5π/3,11π/3,
now 11π/3 >2π
so x=5π/3
Answer:
£39.20
Step-by-step explanation:
2+1+5=8
£78.40/8 = 9.8
9.8*5= 49
49-9.8= 39.2
Answer:
x = 11
Step-by-step explanation:
6x - 21 = 3x + 12
6x - 3x = 21 + 12
3x = 33
x = 33/3
x = 11
Answer:
7.065
Step-by-step explanation:
There are two ways to do this:
(Note: area = pi * r^2)
Method 1:
Diameter of A = 4, so radius = 4/2 = 2
Area of A = 3.14 * 2^2 = 12.56
Diameter of B = 5, so radius = 5/2 = 2.5
Area of B = 3.14 * 2.5^2 = 19.625
Difference in area = 19.625 - 12.56 = 7.065
Method 2:
First find out how much larger the diameter of B is than A, so 5/4 = 1.25.
What this means is if you take the diameter of A and multiply it by 1.25, you get the diameter of B.
When dealing with area, the area of B will be 1.25^2 times bigger than A.
Area of A = 3.14 * 2^2 = 12.56
So area B = 12.56 * 1.25^2 = 19.625
Difference = 19.625 - 12.56 = 7.065
Answer:
the height is 14
Step-by-step explanation:
since the volume in a rect. prism is V = width x height x length, and the width times length is the area of the base, for height we need to do 840/60 to find the height
840/60 = 14
