There will be three pairs of matching sides: one pair 5x7, one pair 5x12 and one pair 12x7. We can compute the are of each side (in pairs) and then add up the total:
2p-b=c-ap solve for tems of p so p=bla bla bla
2 answers:
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Answer:
Options (B) and (E)
Step-by-step explanation:
Area of ΔABC =
=
= 42 in²
Area of trapezoid ADEC =
[Here, and
are the parallel sides and 'h' is the height of the isosceles trapezoid given]
=
= 96 in²
Area of the pentagon = Area of triangle ABC + Area of trapezoid ADEC
= 42 + 96
= 138 in²
Therefore, Options (B) and (E) are the correct options.
Derivative of the denominator:
Hmm our numerator is 2x+7. Ok this let's us know that a simple u-substitution is NOT going to work. But let's apply some clever Algebra to the numerator splitting it up into two separate fractions. Split the +7 into +2 and +5.
and then split the fraction,
Based on our previous test, we know that a simple substitution will work for the first integral:
So the first integral changes,
integrating to a log,
Other one is a little tricky. We'll need to complete the square on the denominator. After that it will look very similar to our arctangent integral so perhaps we can just match it up to the identity.
So we have this going on,
Let's factor the 5 out of the intergral,
and the 4 from the denominator,
Bringing all that stuff together as a single square,
Making the substitution:
giving us,
simplying a lil bit,
and hopefully from this point you recognize your arctangent integral,
undo your substitution as a final step,
and include a constant of integration,
Hope that helps!
Lemme know if any steps were too confusing.