Answer:
A ≈ 75 in²
Step-by-step explanation:
the area (A) of the circle is calculated as
A = πr² ( r is the radius )
here r = 5 and using 3 for π , then
A = 3 × 5² = 3 × 25 = 75 in²
3(1/2)+y = -8
Okay, so half of 3 is 1.5.
Then the equation is 1.5+y=-8.
Now you subtract -8 by 1.5.
You should get -9.5, and I believe that is correct. You can check the answer by replacing y with -9.5.
The nth term is (presuming the denominator on the first is a typo)
![-\dfrac{n}{(-3)^n}](https://tex.z-dn.net/?f=-%5Cdfrac%7Bn%7D%7B%28-3%29%5En%7D)
The ratio of successive terms is
![\dfrac{ \frac{n+1}{(-3)^(n+1)}}{\frac{n}{(-3)^n}} = \frac{n+1}{-3n}](https://tex.z-dn.net/?f=%5Cdfrac%7B%20%5Cfrac%7Bn%2B1%7D%7B%28-3%29%5E%28n%2B1%29%7D%7D%7B%5Cfrac%7Bn%7D%7B%28-3%29%5En%7D%7D%20%3D%20%5Cfrac%7Bn%2B1%7D%7B-3n%7D)
The limit is -1/3, absolute value less than 1, so the series converges. It has a sum -- that's what converges means.
Answer:
<em>7</em><em>,</em><em>0</em><em>8</em><em>0</em><em>,</em><em>0</em><em>7</em><em>3</em><em> </em>
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Answer:
<em>The length of RS is 47 units</em>
Step-by-step explanation:
<u>Midsegment Theorem</u>
The midsegment of a trapezoid is a line segment that connects the midpoints of the non-parallel sides.
The length of the midsegment of a trapezoid is the average of the lengths of the bases.
The midsegment of the given trapezoid is VW, and the bases are RS and UT.
According to the midsegment theorem:
![\displaystyle VW=\frac{RS+UT}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20VW%3D%5Cfrac%7BRS%2BUT%7D%7B2%7D)
Substituting the variable lengths of the sides:
![\displaystyle 3x+5=\frac{2x+15+6x-37}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%203x%2B5%3D%5Cfrac%7B2x%2B15%2B6x-37%7D%7B2%7D)
Operating:
![\displaystyle 3x+5=\frac{8x-22}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%203x%2B5%3D%5Cfrac%7B8x-22%7D%7B2%7D)
Dividing the fraction:
![3x+5=4x-11](https://tex.z-dn.net/?f=3x%2B5%3D4x-11)
Rearranging:
![4x-3x=5+11](https://tex.z-dn.net/?f=4x-3x%3D5%2B11)
Operating:
x=16
The length of RS is:
![RS=2x+15=2*16+15=32+15=47](https://tex.z-dn.net/?f=RS%3D2x%2B15%3D2%2A16%2B15%3D32%2B15%3D47)
The lenght of RS is 47 units