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
Answer: Zoey needs 168 square feet if carpet squares.
Step-by-step explanation:
Zoey wants to cover her bedroom floor with carpet squares. Each square has an area of 1 square foot.
The formula for determining the area of a rectangle is expressed as
Area = length × width
Her bedroom measures 12 feet by 14 feet. Therefore, the area of her bedroom would be
12 × 14 = 168 square feet.
Therefore, the number of carpet squares that Zoey needs would be
168/1 = 168 square feet
Answer: 40 degrees
Step-by-step explanation:
The 3 angles of a triangle must add up to 180 degrees.
Let's say this is triangle ABC and angle A has a measure of 100 degrees.
That leaves 80 degrees to be split evenly between angles B and C.
80/2 = 40, so angles B and C must each be 40 degrees.
Answer:
∠KMN = 66°
Step-by-step explanation:
In ΔKMN,
∠MKN + ∠KNM + ∠KMN = 180 {Angle sum property of triangle}
39 + 75 + ∠KMN = 180
114 + ∠KMN = 180
∠KMN = 180 - 114
∠KMN = 66°
