Answer:
Part 1) The exact value of the arc length is \frac{25}{6}\pi \ in
Part 2) The approximate value of the arc length is 13.1\ in
Step-by-step explanation:
ind the circumference of the circle
The circumference of a circle is equal to
C=2\pi r
we have
r=5\ in
substitute
C=2\pi (5)
C=10\pi\ in
step 2
Find the exact value of the arc length by a central angle of 150 degrees
Remember that the circumference of a circle subtends a central angle of 360 degrees
by proportion
\frac{10\pi}{360} =\frac{x}{150}\\ \\x=10\pi *150/360\\ \\x=\frac{25}{6}\pi \ in
Find the approximate value of the arc length
To find the approximate value, assume
\pi =3.14
substitute
\frac{25}{6}(3.14)=13.1\ in
Your answer to your question is 51
begin by pulling 2 out of the numerator using the distributive property.
numerator: 2(16x^4 - 25) and now factor
numerator: 2(4x^2 - 5)(4x^2 + 5)
Now go to the denominator. It looks messy but it will break down.
Pull out 4x^2 for the first two terms and 5 for the last 2 terms. Use the distributive property.
denominator: 4x^2(x - 3) - 5(x - 3) now x - 3 is the common term.
denominator: (x - 3)(4x^2 - 5)
Put the two results together.
After canceling out 4x^2 - 5 on both the numerator and the denominator, you are left with.
