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3 years ago

14

In parallelogram MNOP PK = 5x and KN = x2-14 what is PN?

1 answer:

enyata [817]3 years ago

5 0

Answer:

$|PN|=70$

Step-by-step explanation:

The diagonals of a parallelogram bisect each other.

This implies that;

$|PK|=|KN|$

$5x=x^2-14$

We group all terms on the right hand side to obtain;

$0=x^2-5x-14$

$\Rightarrow x^2-5x-14=0$

Factor;

$\Rightarrow x^2-7x+2x-14=0$

$\Rightarrow x(x-7)+2(x-7)=0$

$\Rightarrow (x-7)(x+2)=0$

$\Rightarrow (x-7)=0,(x+2)=0$

$\Rightarrow x=7,x=-2$

We discard the negative value.

$\Rightarrow x=7$

$|PN|=2|PK|$

$|PN|=2(5(7))$

$|PN|=70$

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<img src="https://tex.z-dn.net/?f=%24a%2Ba%20r%2Ba%20r%5E%7B2%7D%2B%5Cldots%20%5Cinfty%3D15%24%24a%5E%7B2%7D%2B%28a%20r%29%5E%7B

riadik2000 [5.3K]

Let

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and subtracting this from $S_n$ gives

$(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}$

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Now, we're given

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We must have |r| < 1 since both sums converge, so

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Solving for r by substitution, we have

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which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

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