acknowledgement for disaster management file for thanking god
Answers
Explanation:
» Four numbers are in AP whose sum is 40.
• Let four numbers be (a - 3d), (a - d), (a + d), (a + 3d)
A.T.Q.
=> a - 3d + a - d + a + d + a + 3d = 40
=> 4a = 40
=> a = 40/4
=> a = 10 _______ (eq 1)
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» The ratio of the product of first and fourth term is 2:3.
\dfrac{a \: - \: 3d}{a \: + \: 3d} \: = \: \dfrac{2}{3}
a+3d
a−3d
=
3
2
Cross-multiply them..
=> 3(a - 3d) = 2(a + 3d)
=> 3a - 9d = 2a + 6d
=> 3(10) - 9d = 2(10) + 6d [From (eq 1)]
=> 30 - 9d = 20 + 6d
=> 30 - 20 = 6d + 9d
=> 10 = 15d
=> d = 10/15
=> d = 2/3 ________ (eq 2)
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» We have to find the numbers. (Means AP.)
• a - 3d = 10 - 3(2/3)
=> 10 - 2 = 8
• a - d = 10 - 2/3
=> (30 - 2)/3 = 28/3
• a + d = 10 + 2/3
=> (30 + 2)/3 = 32/3
• a + 3d = 10 + 3(2/3)
=> 10 + 2 = 12
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\textbf{Number are : 8, 28/3, 32/3 and 12}Number are : 8, 28/3, 32/3 and 12
__________ [ANSWER]
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✡ From above calculations we get numbers 8, 28/3, 32/3 and 12
Add all the numbers.
=> 8 + 28/3 + 32/3 + 12
=> (24 + 28 + 32 + 28)3
=> 120/3
=> 40
_______ [HENCE VERIFIED]
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I am very thankful to everyone who all supported me, for I have completed my project effectively and moreover on time. I am over helped in all humbleness and gratefulness to acknowledge my depth to all those who have helped me to put these ideas well.
I am equally grateful to my (Subject) teacher (Name). She gave me moral support and guided me in different matters regarding the topic. With the help of her valuable suggestions, guidance and encouragement, I was able to perform this project work.
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