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nalin [4]
3 years ago
8

you are out with friends. half of you want to go bowling and the other half want to go to a movie. how will you make a fair deci

sion
Mathematics
1 answer:
andre [41]3 years ago
3 0

Answer:

you can toss a coin half the gruop picks heads and the other tails

Step-by-step explanation:


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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
PLEASE HURRY 12 POINTS PLEASE HELPPPPPP
GalinKa [24]

Step-by-step explanation:

to find the area of a circle, it is pi times radius squared. so 1 times pi squared is pi^2 the area is 4 plus 2pi^2

6 0
2 years ago
The expression 14.50x can be used to find the total cost for x tickets on Family Night for admission and the movie. What is the
sp2606 [1]
All you have to do is substitute x for 3.
You get:
14.50 times 3

14.50 times 3 is 43.50

The answer is $14.50
6 0
3 years ago
Rosa recorded the height (in centimeters) of a pea plant over a ten day period for a science experiment.
notka56 [123]
I think that
The answer is A
y=2.0×(1.4^x)
4 0
3 years ago
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Identify the mapping diagram that represents the relation and determine whether the relation is a function. {(–8, –6), (–5, 2),
SashulF [63]
Do you have the answer options? Sorry, can't answer without them ):
8 0
3 years ago
Read 2 more answers
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