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Ulleksa [173]
3 years ago
6

write a linear equation that intersects y=x^2 at two points. Then write a second linear equation that intersects y=x^2 at just o

ne point, and a third linear that does not intersect y=x^2. Explain how you found the linear equations.
Mathematics
1 answer:
Liula [17]3 years ago
5 0

We know that y = x^2 is a parabola, concave up, with vertex in the origin (0,0)

So, we may use three horizontal lines for our purpose: any horizontal line above the x axis will intersect the parabola twice. The x axis itself intersects the parabola once on the vertex, while any horizontal line below the x axis won't intercept the parabola.

Here's the examples:

  • The horizontal line y = 4 intercepts the parabola twice: the system y = x^2,\ y = 4 is solved by x^2=4 \implies x = \pm 2
  • The horizontal line y=0 intercepts the parabola only once: the system is y=x^2,\ y=0 which yields x^2=0\implies x=0 which is a repeated solution
  • The horizontal line y=-5 intercepts the parabola only once: the system is y=x^2,\ y=-5 which yields x^2=-5 which is impossible, because a squared number can't be negative.
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Consider the points below. P(2, 0, 2), Q(−2, 1, 4), R(7, 2, 6)
Zina [86]

Answer: the vector orthogonal is  ( 0, 26, -13 )

Step-by-step explanation:

Given that;

P(2, 0, 2),  Q(−2, 1, 4), R(7, 2, 6)

PQ = Q - P = (−2, 1, 4) - (2, 0, 2) = (-4, 1, 2)

PR = R - P = (7, 2, 6)  - (2, 0, 2) = ( 5, 2, 4)

SO

orthogonal vector = PQ × PR

= ║ i    j    k

    -4   1   2          = i(1×4 - 2×2) + j(5×2 - (-4×4)) + k(-4×2 - 5×1) = 0i + 26j - 13k

     5   2   4  ║

= ( 0, 26, -13 )

Therefore the vector orthogonal is  ( 0, 26, -13 )

3 0
3 years ago
Mount Everest is over 2.9 × 10 4 feet tall. In standard form, that is
just olya [345]

Answer:

29000 feet

Step-by-step explanation:

Move decimal points 4 places to the right.

8 0
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Answer: which question

Step-by-step explanation:

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Expand and simplify 3(2a+3b)+2(a+2b)
ICE Princess25 [194]

Answer:

8a+13b

Step-by-step explanation:

First start by multiplying the coefficient with the parantheses.

3(2a+3b)+2(a+2b)

6a+9b+2a+4b

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This equation cannot be further simplified.

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3 years ago
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A house was bought for £100,000
jolli1 [7]

Answer:

122500

Step-by-step explanation:

The formula

A=p(1+rt)

A ?

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T 3 years

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3 years ago
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