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Naily [24]
3 years ago
14

D) Vivek is 30 years younger than his father. After 10 years their ages will be in the ratio 1:2. Find their present ages.​

Mathematics
2 answers:
tangare [24]3 years ago
6 0

Answer:

I think Vivek is 20 and his father is 50

Because 30 + 30 equals 60 as he has to be half his age he'll be 30 but that's in 10 years time. you just subtract 30 and 60 by 10 and you'll get 20 and 50

pychu [463]3 years ago
3 0

Answer:

Vivek:20 years

Father:50 years

Step-by-step explanation:

Since it is a age question, their difference do not change, so

2-1=1 (difference in ratio)

1u=30

Vivek now:30-10=20 years

Father: 30x2=60

60-10=50 years

Hope this helps! Thanks.

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Find the point on the parabola y^2 = 4x that is closest to the point (2, 8).
guapka [62]

Answer:

(4, 4)

Step-by-step explanation:

There are a couple of ways to go at this:

  1. Write an expression for the distance from a point on the parabola to the given point, then differentiate that and set the derivative to zero.
  2. Find the equation of a normal line to the parabola that goes through the given point.

1. The distance formula tells us for some point (x, y) on the parabola, the distance d satisfies ...

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Differentiating with respect to x and setting dd/dx=0, we have ...

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We can factor 2 from this to get

... 0 = x -2 +(y -8)(dy/dx)

Differentiating the parabola's equation, we find ...

... 2y(dy/dx) = 4

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Substituting for x (=y²/4) and dy/dx into our derivative equation above, we get

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2. The derivative above tells us the slope at point (x, y) on the parabola is ...

... dy/dx = 2/y

Then the slope of the normal line at that point is ...

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The normal line through the point (2, 8) will have equation (in point-slope form) ...

... y - 8 = (-y/2)(x -2)

Substituting for x using the equation of the parabola, we get

... y - 8 = (-y/2)(y²/4 -2)

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... 8y -64 = -y³ +8y

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... x = y²/4 = 4

The point on the parabola that is closest to the point (2, 8) is (4, 4).

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