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Inessa05 [86]
3 years ago
11

I did a little bit but i need help

Mathematics
1 answer:
Lilit [14]3 years ago
4 0

Answer:

Input is the number in the first column of the table. This is the number that you start with to follow the rule if the rule is given. You would also use this number to figure out what the rule is if it is not given.

Step-by-step explanation:

An input-output table, like the one shown below, can be used to represent a function. Each pair of numbers in the table is related by the same function rule. That rule is: multiply each input number (\begin{align*}x\end{align*}-value) by 3 to find each output number (\begin{align*}y\end{align*}-value).

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F(x)=2x an$ g(x)=2x+3,what is the value of f(g(-8))
Fudgin [204]

First plug in g(x) into f(x)

F((g(x))=2(2x+3)

And now you plug in -8

F(g(-8))=2(-16+3)

F(g(-8))=2(-13)

F(g(-8))=-26

6 0
2 years ago
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
2 years ago
a fruit salad contains 20 different pieces of fruit. there are 3 pieces of apple, 8 pieces of watermelon, 7 pieces of banana, an
Neko [114]
There are 2 oranges, if that’s what the question was?
8 0
2 years ago
Read 2 more answers
There was a bus that hit there was 2 married people and ten other passengers every single person died. how many people are alive
musickatia [10]

Answer:

2 people are are alive because all the single people(meaning they have no spouse) died do the married people are the only ones who survived.

Step-by-step explanation:

4 0
3 years ago
A teacher's age is 6years greater then 2 times a students age.a principals age is 10 years greater than 3 times the students age
snow_tiger [21]

Answer: 4x + 5

Step-by-step explanation:

6 0
2 years ago
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