Answer: 1384.74
Step-by-step explanation:
A=πr^2
radius=42/2=21
(3.14)(21)^2
3.14(441)
1384.74
Answer: x = 14/23
Step-by-step explanation:
3x-6=4(2-3x)-8x
3x-6=8-12x-8x --> Expand 4(2-3x)
3x-6=8-20x --> Collect like terms
3x-6+6=8-20x+6 --> Add 6 to both sides, to remove it from the right side
3x=-20x+14
3x+20x=-20x+14+20x --> Add 20x to both sides, to remove it from the left side
23x=14
--> Divide both sides by 23
x = 14/23
<span>No, because postulates are assumptions. Some true, some not. So it can't be used to prove it</span>
The question is somewhat poorly posed because the equation doesn't involve <em>θ</em> at all. I assume the author meant to use <em>x</em>.
sec(<em>x</em>) = csc(<em>x</em>)
By definition of secant and cosecant,
1/cos(<em>x</em>) = 1/sin(<em>x</em>)
Multiply both sides by sin(<em>x</em>) :
sin(<em>x</em>)/cos(<em>x</em>) = sin(<em>x</em>)/sin(<em>x</em>)
As long as sin(<em>x</em>) ≠ 0, this reduces to
sin(<em>x</em>)/cos(<em>x</em>) = 1
By definition of tangent,
tan(<em>x</em>) = 1
Solve for <em>x</em> :
<em>x</em> = arctan(1) + <em>nπ</em>
<em>x</em> = <em>π</em>/4 + <em>nπ</em>
(where <em>n</em> is any integer)
In the interval 0 ≤ <em>x</em> ≤ 2<em>π</em>, you get 2 solutions when <em>n</em> = 0 and <em>n</em> = 1 of
<em>x</em> = <em>π</em>/4 <u>or</u> <em>x</em> = 5<em>π</em>/4