The square root of 49 = 7 if it is multiplied by 14 and divided by pi, it would equal 31.194, which would be 31.19.
Answer:
The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h.
Step-by-step explanation:
We have:
The generic equation of the line is: y-yo = m (x-xo)
The slope is:
m = (y2-y1) / (x2-x1)
m = (- 2-0) / (3-0)
m = -2 / 3
We choose an ordered pair
(xo, yo) = (0, 0)
Substituting values:
y-0 = (- 2/3) (x-0)
Rewriting:
y = (- 2/3) x
Answer:
The equation of the line is:
y = (- 2/3) x
Given:
The sum of two terms of GP is 6 and that of first four terms is ![\dfrac{15}{2}.](https://tex.z-dn.net/?f=%5Cdfrac%7B15%7D%7B2%7D.)
To find:
The sum of first six terms.
Solution:
We have,
![S_2=6](https://tex.z-dn.net/?f=S_2%3D6)
![S_4=\dfrac{15}{2}](https://tex.z-dn.net/?f=S_4%3D%5Cdfrac%7B15%7D%7B2%7D)
Sum of first n terms of a GP is
...(i)
Putting n=2, we get
![S_2=\dfrac{a(1-r^2)}{1-r}](https://tex.z-dn.net/?f=S_2%3D%5Cdfrac%7Ba%281-r%5E2%29%7D%7B1-r%7D)
![6=\dfrac{a(1-r)(1+r)}{1-r}](https://tex.z-dn.net/?f=6%3D%5Cdfrac%7Ba%281-r%29%281%2Br%29%7D%7B1-r%7D)
...(ii)
Putting n=4, we get
![S_4=\dfrac{a(1-r^4)}{1-r}](https://tex.z-dn.net/?f=S_4%3D%5Cdfrac%7Ba%281-r%5E4%29%7D%7B1-r%7D)
![\dfrac{15}{2}=\dfrac{a(1-r^2)(1+r^2)}{1-r}](https://tex.z-dn.net/?f=%5Cdfrac%7B15%7D%7B2%7D%3D%5Cdfrac%7Ba%281-r%5E2%29%281%2Br%5E2%29%7D%7B1-r%7D)
![\dfrac{15}{2}=\dfrac{a(1+r)(1-r)(1+r^2)}{1-r}](https://tex.z-dn.net/?f=%5Cdfrac%7B15%7D%7B2%7D%3D%5Cdfrac%7Ba%281%2Br%29%281-r%29%281%2Br%5E2%29%7D%7B1-r%7D)
(Using (ii))
Divide both sides by 6.
Taking square root on both sides, we get
![\pm 0.5=r](https://tex.z-dn.net/?f=%5Cpm%200.5%3Dr)
Case 1: If r is positive, then using (ii) we get
The sum of first 6 terms is
![S_6=\dfrac{4(1-(0.5)^6)}{(1-0.5)}](https://tex.z-dn.net/?f=S_6%3D%5Cdfrac%7B4%281-%280.5%29%5E6%29%7D%7B%281-0.5%29%7D)
![S_6=\dfrac{4(1-0.015625)}{0.5}](https://tex.z-dn.net/?f=S_6%3D%5Cdfrac%7B4%281-0.015625%29%7D%7B0.5%7D)
![S_6=8(0.984375)](https://tex.z-dn.net/?f=S_6%3D8%280.984375%29)
![S_6=7.875](https://tex.z-dn.net/?f=S_6%3D7.875)
Case 2: If r is negative, then using (ii) we get
The sum of first 6 terms is
![S_6=\dfrac{12(1-(-0.5)^6)}{(1+0.5)}](https://tex.z-dn.net/?f=S_6%3D%5Cdfrac%7B12%281-%28-0.5%29%5E6%29%7D%7B%281%2B0.5%29%7D)
![S_6=\dfrac{12(1-0.015625)}{1.5}](https://tex.z-dn.net/?f=S_6%3D%5Cdfrac%7B12%281-0.015625%29%7D%7B1.5%7D)
![S_6=8(0.984375)](https://tex.z-dn.net/?f=S_6%3D8%280.984375%29)
![S_6=7.875](https://tex.z-dn.net/?f=S_6%3D7.875)
Therefore, the sum of the first six terms is 7.875.
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