Answer:
R=0.42857
Step-by-step explanation:
ac/question, -6+2R+12R=0
14R=6
R=![\frac{6}{14}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B14%7D)
R=0.42857
5. c = 13
6. b=6
7. b=8
8. a=30
9. a=2√3
Step-by-step explanation:
We will use Pythagorean theorem in each to find the length of missing side.
![a^2+b^2=c^2](https://tex.z-dn.net/?f=a%5E2%2Bb%5E2%3Dc%5E2)
5. a=12, b=5
Putting in formula
![(12)^2+(5)^2=c^2\\144+25=c^2\\169=c^2\\c^2=169](https://tex.z-dn.net/?f=%2812%29%5E2%2B%285%29%5E2%3Dc%5E2%5C%5C144%2B25%3Dc%5E2%5C%5C169%3Dc%5E2%5C%5Cc%5E2%3D169)
Taking square root on both sides
![\sqrt{c^2}=\sqrt{169}\\c=13](https://tex.z-dn.net/?f=%5Csqrt%7Bc%5E2%7D%3D%5Csqrt%7B169%7D%5C%5Cc%3D13)
Therefore,
c = 13
6. a=8 , c=10
Putting in formula
![(8)^2+b^2=(10)^2\\64+b^2=100\\b^2=100-64\\b^2=36\\](https://tex.z-dn.net/?f=%288%29%5E2%2Bb%5E2%3D%2810%29%5E2%5C%5C64%2Bb%5E2%3D100%5C%5Cb%5E2%3D100-64%5C%5Cb%5E2%3D36%5C%5C)
Taking square root on both sides
![\sqrt{b^2}=\sqrt{36}\\b=6](https://tex.z-dn.net/?f=%5Csqrt%7Bb%5E2%7D%3D%5Csqrt%7B36%7D%5C%5Cb%3D6)
b=6
7. a=15, c=17
Putting in formula
![(15)^2+b^2=(17)^2\\225+b^2=289\\b^2=289-225\\b^2=64](https://tex.z-dn.net/?f=%2815%29%5E2%2Bb%5E2%3D%2817%29%5E2%5C%5C225%2Bb%5E2%3D289%5C%5Cb%5E2%3D289-225%5C%5Cb%5E2%3D64)
Taking square root on both sides
![\sqrt{b^2}=\sqrt{64}\\b=8](https://tex.z-dn.net/?f=%5Csqrt%7Bb%5E2%7D%3D%5Csqrt%7B64%7D%5C%5Cb%3D8)
b=8
8. b=40, c=50
Putting in formula
![a^2+(40)^2=(50)^2\\a^2+1600=2500\\a^2=2500-1600\\a^2=900](https://tex.z-dn.net/?f=a%5E2%2B%2840%29%5E2%3D%2850%29%5E2%5C%5Ca%5E2%2B1600%3D2500%5C%5Ca%5E2%3D2500-1600%5C%5Ca%5E2%3D900)
Taking square root on both sides
![\sqrt{a^2}=\sqrt{900}\\a=30](https://tex.z-dn.net/?f=%5Csqrt%7Ba%5E2%7D%3D%5Csqrt%7B900%7D%5C%5Ca%3D30)
a=30
9. b=2 , c=4
Putting in formula
![a^2+(2)^2=(4)^2\\a^2+4=16\\a^2=16-4\\a^2=12](https://tex.z-dn.net/?f=a%5E2%2B%282%29%5E2%3D%284%29%5E2%5C%5Ca%5E2%2B4%3D16%5C%5Ca%5E2%3D16-4%5C%5Ca%5E2%3D12)
Taking square root on both sides
![\sqrt{a^2}=\sqrt{12}\\\sqrt{a^2}=\sqrt{2*2*3}\\a=2\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7Ba%5E2%7D%3D%5Csqrt%7B12%7D%5C%5C%5Csqrt%7Ba%5E2%7D%3D%5Csqrt%7B2%2A2%2A3%7D%5C%5Ca%3D2%5Csqrt%7B3%7D)
a=2√3
Keywords: square root, pythagorean theorem
Learn more about square root at:
#LearnwithBrainly
Answer:
44
Step-by-step explanation:
1. Since point V is the midpoint of line MP, VP is half of MP.
2. Since VP is half of MP, 2(4x-6) = 6x+2
3. ![\frac{2(4x-6)}{2} =\frac{6x+2}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2%284x-6%29%7D%7B2%7D%20%3D%5Cfrac%7B6x%2B2%7D%7B2%7D)
4. 4x-6 = 3x+1
5. x = 7
6. Substitute x with 7 on equation 6x+2. 6(7)+2
7. Answer 44.
Answer:
![\pm 9in^2](https://tex.z-dn.net/?f=%5Cpm%209in%5E2)
Step-by-step explanation:
We are given that
Radius of end of a log, r= 9 in
Error,
in
We have to find the error in computing the area of the end of the log by using differential.
Area of end of the log, A=![pi r^2](https://tex.z-dn.net/?f=pi%20r%5E2)
![\frac{dA}{dr}=2\pi r](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdr%7D%3D2%5Cpi%20r)
![\frac{dA}{dr}=2\pi (9)=18\pi in^2](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdr%7D%3D2%5Cpi%20%289%29%3D18%5Cpi%20in%5E2)
Now,
Approximate error in area
![dA=\frac{dA}{dr}(\Delta r)](https://tex.z-dn.net/?f=dA%3D%5Cfrac%7BdA%7D%7Bdr%7D%28%5CDelta%20r%29)
Using the values
![dA=18\pi (\pm 1/2)](https://tex.z-dn.net/?f=dA%3D18%5Cpi%20%28%5Cpm%201%2F2%29)
![\Delta A\approx dA=\pm 9in^2](https://tex.z-dn.net/?f=%5CDelta%20A%5Capprox%20dA%3D%5Cpm%209in%5E2)
Hence, the possible propagated error in computing the area of the end of the log![=\pm 9in^2](https://tex.z-dn.net/?f=%3D%5Cpm%209in%5E2)