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IrinaK [193]
3 years ago
14

Please help!! please please

Mathematics
1 answer:
Leona [35]3 years ago
5 0
I honestly don'y know i'm really sorry.

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A circle has centre (3,0) and radius 5. The line y = 2x + k intersects the circle in two points. Find the set
lara [203]

A circle with center (3,0) and radius 5 has equation

(x-3)^2+y^2=25 \iff x^2 + y^2- 6 x  = 16

If we substitute y=2x+k in this equation, we have

x^2+(2x+k)^2-6x=16 \iff 5x^2+(4k-6)x+k^2-16=0

This equation has two solutions (i.e. the line intersects the circle in two points) if and only if the determinant is greater than zero:

\Delta=b^2-4ac=(4k-6)^2-4\cdot 5\cdot (k^2-16)>0

The expression simplifies to

-4 (k^2 + 12 k - 89)>0 \iff k^2 + 12 k - 89

The solutions to the associated equation are

k^2 + 12 k - 89=0 \iff k=-6\pm 5\sqrt{5}

So, the parabola is negative between the two solutions:

-6-5\sqrt{5}

8 0
3 years ago
Does question 4 look correct
mars1129 [50]
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2 years ago
What are the coordinates of the image of vertex D after a reflection across the x-axis?
alex41 [277]

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Where is the image

Step-by-step explanation:

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Hich values are solutions to the inequality?
Troyanec [42]

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So, in the list of numbers, 8 and 9 are solutions

7 0
3 years ago
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