Answer:
y = 6
Step-by-step explanation:
Given that y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 3 when x = 9, then
k = 
= 
= 
, thus
y = x ← equation of variation
When x = 18, then
y = × 18 = 
= 6
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
The given function is a variable separable differential equation. Combine like terms, integrate, apply the appropriate limits, and express V in terms of t. This is done as follows:
dV/dt = -3(V)^1/2
dV/-3V^1/2 = dt
m here is the initial V which is 225. Then after integrating,
-2/3 (√V - √225) = t
-2/3 (√V - 15) = t
That is the expression for V at time t. I hope I was able to help. Have a good day.
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
we know that
The <u><em>Triangle Inequality Theorem</em></u> states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
so
Applying the Triangle Inequality Theorem
1) 
solve for n
Rewrite
2) 
therefore
