√(144*x²) = (√144)*(√x²) = 12x
Answer is D.12x.

Setting

, you have

. Then the integral becomes




Now,

in general. But since we want our substitution

to be invertible, we are tacitly assuming that we're working over a restricted domain. In particular, this means

, which implies that

, or equivalently that

. Over this domain,

, so

.
Long story short, this allows us to go from

to


Computing the remaining integral isn't difficult. Expand the numerator with the Pythagorean identity to get

Then integrate term-by-term to get


Now undo the substitution to get the antiderivative back in terms of

.

and using basic trigonometric properties (e.g. Pythagorean theorem) this reduces to
Answer:
B
Step-by-step explanation:
x is alternate exterior angles and y is 180 - x
Answer:
6.735
Step-by-step explanation:
im smart
Answer:
4.1 billion
Step-by-step explanation:
1 ft = 30.48 cm
1 in = 2.54 cm
The volume of rain that fell on the roof is given by ...
V = LWH
V = (175 ft × 30.48 cm/ft)(45 ft × 30.48 cm/ft)(11 in × 2.54 cm/in)
= 175×45×11×30.48²×2.54 cm³ = 204,412,236.336 cm³
At 20 drops per cm³, this will be ...
20×204,412,236.336 ≈ 4,088,244,727 . . . . raindrops
About 4.1 billion raindrops fell on your roof.