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elena-s [515]
1 year ago
9

Help quick please iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii neeeeedddddddd heeeeeellllppppppppp

Mathematics
1 answer:
UkoKoshka [18]1 year ago
4 0
-9 + pi will be irrational becasue it contains pi
23.2 repeating + sqrt 16 is rational because repeating numbers are rational and sqrt 16 is rational.
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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 ...

... d² = (x -2)² +(y -8)² . . . . . . . the y in this equation is a function of x

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

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

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

... dy/dx = 2/y

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

... 0 = y²/4 -2 +(y -8)(2/y) = y²/4 -16/y

... 64 = y³ . . . . . . multiply by 4y, add 64

... 4 = y . . . . . . . . cube root

... y²/4 = 16/4 = x = 4

_____

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 ...

... -1/(dy/dx) = -y/2

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)

Multiplying by 8 gives ...

... 8y -64 = -y³ +8y

... y³ = 64 . . . . subtract 8y, multiply by -1

... y = 4 . . . . . . cube root

... x = y²/4 = 4

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

4 0
3 years ago
What is the area of a rhombus with dimensions of 22 inches and 10 inches?
docker41 [41]
The answer to the problem is 220
3 0
3 years ago
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Find the area of that with explanations thanks
TEA [102]

Answer:

900m or 300m

Step-by-step explanation:

45 x 20 = 900

30 x 10 = 300

3 0
3 years ago
Read 2 more answers
Two numbers that multiply to -49 and add up to 0
Elenna [48]

The only way to do that is with  +7  and  -7 .

6 0
3 years ago
What is the answer to this question?
mrs_skeptik [129]

Answer:

B

Step-by-step explanation:

Out of the 4 options, we only need 1. Therefore, the probability is \frac{1}{4}

4 0
2 years ago
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