
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:
y = 5
Step-by-step explanation:
The triangles will be congruent when corresponding sides are congruent. __
We already have ...
KL ≅ NP . . . = 15 mm
JL ≅ MP . . . = 22 mm
So, we need ...
JK ≅ MN
4y +12 = 32 . . . . substitute given values
This will be the case when ...
4y = 20 . . . . . subtract 12
y = 5 . . . . . . . divide by 4
The value of y that makes the triangles congruent is 5.
10% of a mile is 528ft, 1 meter is about 3 feet
Answer:
Hello!
After reviewing the question you have provided, I came up with the correct answer:
C) 2
Step-by-step explanation:
Firstly:
As the question states, you need to round each number to the nearest whole number and then choose the closest estimate to what the nearest solution could be.
When you round the two numbers you should come up with "3-1= ____".
This is because you round up with a number has .5 or higher, and you round down when any number has .4 or lower.
So 3.2 rounds to 3
And 1.4 rounds to 1.
With the new equation you can then solve "3-1= 2"!
Hope this helps!
The following system is INCONSISTENT