3.5 cm 8.5 cm 7 cm 9.9 cm
1 answer:
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Hi there!
2x - 4y = 9
Begin by isolating the y variable by moving 2x to the right-hand side of the equation. (Subtract 2x from both sides):
2x - 2x - 4y = 9 - 2x
-4y = 9 - 2x
Further isolate by dividing both sides by -4:
-4y / (-4) = (9 - 2x) / (-4)
y = -9/4 - 2x/(-4)
Simplify further:
y = -9/4 + 1/2x
y = 1/2x - 9/4
The "b" value is the y-intercept, therefore:
x = 0 at y = -9/4
Answer:
+
*LN(|
|) +C
Step-by-step explanation:
we will have to do a trig sub for this
use x=a*tanθ for sqrt(x^2 +a^2) where a=2
x=2tanθ, dx= 2 sec^2 (θ) dθ
this turns into integral(sqrt( [2tanθ]^2 +4) * 2sec^2 (θ) )dθ
the sqrt( [2tanθ]^2 +4) will condense into 2sec^2 (θ) after converting tan^2(θ) into sec^2(θ) -1
then it simplifies into integral(4*sec^3 (θ)) dθ
you will need to do integration by parts to work out the integral of sec^3(θ) but it will turn into (1/2)sec(θ)tan(θ) + (1/2) LN(|sec(θ)+tan(θ)|) +C
then you will need to rework your functions of θ back into functions of x
tanθ will resolve back into (see substitutions) while secθ will resolve into
sec(θ)= is from its ratio identity of hyp/adj where the hyp. is
and adj is 2 (see tan(θ) ratio)
after resolving back into functions of x, substitute ratios for trig functions:
= +
*LN(|
|) +C