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18 Mar 2020, 02:41
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D
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Difficulty:
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The vertical position of an object can be approximated at any given time by the function \(p(t) = rt − 5t^2 + b\), where p(t) is the vertical position in meters, t is the time in seconds, and r and b are constants. If p(2) = 41 and p(5) = 26, what is p(4)?
(A) 24
(B) 26
(C) 39
(D) 41
(E) 45
Are You Up For the Challenge: 700 Level Questions
(A) 24
(B) 26
(C) 39
(D) 41
(E) 45
Are You Up For the Challenge: 700 Level Questions
18 Mar 2020, 03:08
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p(2) = 2r-20+b = 41
2r+b=61......(1)
p(5)= 5r-125+b = 26
5r+b= 151.....(2)
From (1) and (2)
r= 30 and b=1
p(4)= 4r-80+b = 4*30 -80 +1 = 41
2r+b=61......(1)
p(5)= 5r-125+b = 26
5r+b= 151.....(2)
From (1) and (2)
r= 30 and b=1
p(4)= 4r-80+b = 4*30 -80 +1 = 41
Bunuel
23 Aug 2021, 06:33
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Soltuion:
We are given a function \(p(t)=rt−5t^2+b\)
We are also given \(p(2)=41\). This means we can write:
\(⇒ 2r-5\times 2^2+b=41\)
\(⇒ 2r-5\times 4+b=41\)
\(⇒ 2r-20+b=41\)
\(⇒ 2r+b=61\).........\((i)\)
Similarly, we are also given \(p(5)=26\)
\(⇒ 5r-5\times 5^2+b=26\)
\(⇒ 5r-125+b=26\)
\(⇒ 5r+b=151\).........\((ii)\)
Subtracting both the equations we got: \(2r+b-5r-b=61-151\)
\(⇒ -3r=-90\)
\(⇒ 3r=90\)
\(⇒ r=30\)
Plugging \(r=30\) in equation 2 we get: \(5\times 30+b=151\)
\(⇒ 150+b=151\)
\(⇒ b=1\)
Now that we have \(⇒ r=30\) and \(⇒ b=1\), we can get the value of \(p(4)=4r-5\times 4^2+b\)
\(⇒ 4\times 30-80+1\)
\(⇒ 41\)
Hence the right answer is Option D.
We are given a function \(p(t)=rt−5t^2+b\)
We are also given \(p(2)=41\). This means we can write:
\(⇒ 2r-5\times 2^2+b=41\)
\(⇒ 2r-5\times 4+b=41\)
\(⇒ 2r-20+b=41\)
\(⇒ 2r+b=61\).........\((i)\)
Similarly, we are also given \(p(5)=26\)
\(⇒ 5r-5\times 5^2+b=26\)
\(⇒ 5r-125+b=26\)
\(⇒ 5r+b=151\).........\((ii)\)
Subtracting both the equations we got: \(2r+b-5r-b=61-151\)
\(⇒ -3r=-90\)
\(⇒ 3r=90\)
\(⇒ r=30\)
Plugging \(r=30\) in equation 2 we get: \(5\times 30+b=151\)
\(⇒ 150+b=151\)
\(⇒ b=1\)
Now that we have \(⇒ r=30\) and \(⇒ b=1\), we can get the value of \(p(4)=4r-5\times 4^2+b\)
\(⇒ 4\times 30-80+1\)
\(⇒ 41\)
Hence the right answer is Option D.
