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pishuonlain [190]
3 years ago
6

Which of the following are solutions to the system graphed below.

Mathematics
1 answer:
Kisachek [45]3 years ago
4 0
Weird. I think you just need to look if the point falls on the shaded area. But only (-5,5) does ...

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Find the missing value.<br> (√24-√k)(√24+√k)=5
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Answer:

  • <u>k = 19</u>

Step-by-step explanation:

<u>Identity</u>

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<u>Simplifying the LHS (Left Hand Side)</u>

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3 years ago
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Find an equation of the tangent line to the curve 2(x2+y2)2=25(x2−y2) (a lemniscate) at the point (−3,1). An equation of the tan
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2(x^2+y^2)^2=25(x^2-y^2)

Let y=y(x), so that differentiating both sides wrt x gives

4(x^2+y^2)\left(2x+2y\dfrac{\mathrm dy}{\mathrm dx}\right)=25\left(2x-2y\dfrac{\mathrm dy}{\mathrm dx}\right)

If x=-3 and y=1, the above reduces to

40\left(-6+2\dfrac{\mathrm dy}{\mathrm dx}\right)=25\left(-6-2\dfrac{\mathrm dy}{\mathrm dx}\right)\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac9{13}

This is the slope of the tangent line, which has equation

y-1=\dfrac9{13}(x+3)\implies\boxed{y=\dfrac{9x+40}{13}}

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