The equation of a curve is y=f(x). the curve goes through the points (1,3) and (3,7). f'(x) = 4x+p, where p is a number.

1 answer:

5 0

$f'(x)=4x+p\\
f(x)=2x^2+px+C\\\\
3=2\cdot1^2+p\cdot1+C\\
7=2\cdot3^2+p\cdot3+C\\\\
3=2+p+C\\
7=18+3p+C\\\\
C=1-p\\
3p=-11-C\\\\
3p=-11-(1-p)\\
3p=-11-1+p\\
2p=-12\\
p=-6\\\\
C=1-(-6)\\
C=7\\\\
y=2x^2-6x+7
$

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Can someone help me with this?

Anna35 [415]

Answer:

Let 'a' be the first term, 'r' be the common ratio and 'n' be the number of terms

Series = 2+6+18.......= 2+2•3¹+ 2•3².......= 728

Now,

$Sum = \frac{a( {r}^{n} - 1) }{(r - 1)} \\$

So,

$\frac{a( {r}^{n} - 1)}{(r - 1)} = 728 \\ \frac{2( {3}^{n} - 1) }{(3 - 1)} = 728 \\ \frac{2( {3}^{n} - 1) }{2} = 728 \\ {3}^{n} - 1 = 728 \\ {3}^{n}=728+1\\ {3}^{n} = 729 \\ {3}^{n} = {3}^{6} \\ \boxed{ n = 6}$

Therefore, number of terms is 6

6 is the right answer.

3 0

2 years ago

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DochEvi [55]

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